Geometry
Introduction to Euclidean geometry
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Lines, line segments, and rays
Difference between lines, line segments, and rays
Discussion and questions for this video
 What I want to do in this video is
 think about the difference between a line segment, a line,
 and a ray.
 And this is the pure geometrical versions of these things.
 And so, a line segment is actually probably
 what most of us associate with a line in our everyday lives.
 A line segment is something just like that.
 For lack of a better word, a straight line.
 But why we call it a segment is that it actually
 has a starting and a stopping point.
 So, most of the lines that we experience
 in our everyday reality are actually
 line segments when we think of it
 from a pure geometrical point of view.
 and I know I drew a little bit of a curve here,
 but this is supposed to be completely straight,
 but this is a line segment.
 The segment is based on the fact that it
 has an ending point and a starting point,
 or a starting point and an ending point.
 A line, if you're thinking about it
 in the pure geometric sense of a line, is essentially,
 it does not stop.
 It doesn't have a starting point and an ending point.
 It keeps going on forever in both directions.
 So a line would look like this.
 And to show that it keeps on going on
 forever in that direction right over there, we draw this arrow,
 and to keep showing that it goes on forever
 in kind of the down left direction,
 we draw this arrow right over here.
 So obviously, I've never encountered something
 that just keeps on going straight forever.
 But in math that's the neat thing about math
 we can think about these abstract notions.
 And so the mathematical purest geometric sense of a line
 is this straight thing that goes on forever.
 Now, a ray is something in between.
 A ray has a well defined starting point.
 So that's its starting point, but then
 it just keeps on going on forever.
 So the ray might start over here,
 but then it just keeps on going.
 So that right over there is a ray.
 Now, with that out of the way, let's actually
 try to do the Khan Academy module
 on recognizing the difference between line segments, lines,
 and rays.
 And I think you'll find it pretty straightforward based
 on our little classification right over here.
 So, let me get the module going.
 Where did I put it?
 There you go.
 All right.
 So what is this thing right over here?
 Well, it has two arrows on both ends,
 so it's implying that it goes on forever.
 So this is going to be a line.
 Let's check our answer.
 Yeah, it's a line.
 Now it's taking some time, oh, correct, next question.
 All right, now what about this thing?
 Well, once again, arrows on both sides.
 It means that this thing is going
 to go on forever in both directions.
 So once again, it is a line.
 Fair enough.
 Let's do another one.
 Here we have one arrow, so it goes on forever
 in this direction, but it has a welldefined starting point.
 So it starts there, and then goes on forever.
 And if you remember, that's what a ray is.
 One starting point, but goes on forever.
 Or one way to think about it, goes on forever
 in only one direction.
 So that is a ray.
 So let's do another question.
 This right over here, you have a starting point and an ending
 point, or you could call this the start point and the ending
 point, but it doesn't go on forever in either direction.
 So this right over here is a line segment.
 There you go.
 So hopefully that gives you enough to work
 your way through this module.
 And you might notice, when I did this module right here,
 there is no video.
 And that's exactly what this video is.
 It's the video for this module.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

Have something that's not a question about this content? 
This discussion area is not meant for answering homework questions.
would an infinite line and an infinite ray be equally long? That's my question.
Yes. It's a tricky concept because it feels like an infinitely long ray is only half as long as an infinitely long line. But technically, half of infinity is still infinity.
no, look at set theory as an example. if there is a set that extends infinitely to all the positive numbers, and then there is a set that extends infinitely in both directions, with negative numbers and positive numbers, they are not equal set, because even though both are infinite, you cannot match up each element os the positive set with each element of the negative set. In other words, for every centimeter of the ray, there would be twice as many centimeter of line, therefore the line is longer
The definition of something that is infinite, is that it never ends. As someone else said, half of something that is infinite is still infinite. Think of it this way: If you have something that never ends,no matter how many times you divide it, it will still go on forever. You cannot simply put it into "real life" examples relating to us here on Earth.
Quite an interesting discussion here. Are we are even measuring it in reality at all, or as solely a mathematical concept? In the real physical world, I would think it depends on if space itself is curved or flat. I don't think curved space could be infinite. But I'm not an astrophysicist, just offering my two cents.
@Stuart Wickard, you cannot compare infinity=infinity/2 TO 1=1/2, because as one is an actual or definite number, infinity is more of a concept or an estimate, and nobody knows what a half of it is. that's why infinity divided by two is still an infinite number(infinity)
不相同，直线与射线是2个概念的，射线有起始点
A line is an entirely different concept as a ray. It cannot be answered fully no matter what you do, but if necessary, you should think about the following. The answer depends on whether you are using Euclidian or nonEuclidian geometry. It further depends on whether you are using practical or theoretical science. In Euclidian geometry, the ray would not meet its starting point from the other side like you would if you went around the world. Therefor, in practical science the line would be longer than the ray. However, since infinite means going on forever, the ray would go on forever and so would the line, they would be the same length in theoretical science! In nonEuclidian geometry, the ray would basically wrap around the universe like you might wrap around the world. Therefor, in that case it would meet itself from the other side, and so pass through the same points as the line would, so in practical science they would be the same length. But in theoretical science, the line would cover twice the universe's length by the time the ray would cover the universe's length once, so in theoretical science, the line would be longer. If you see this question on a math test, writing down that both are true or neither are true or even that it is impossible to answer would be good, but you should explain why too. Does this help?
I would say not because the line goes infinite in both directions and a ray would go in one direction,so if you then stop it the line will be longer.Hope this helped!:D
They would, because only one side of a ray goes on to infinity, double infinity (which is what happens with a line) is still the same as normal infinity. So yes, a ray and a line going on forever would be the same length as each other.
no because a line does not stop a ray starts from one point,but a line just goes on forever
it is a tricky concept.it feels like an infinitely long ray is only half as long as an infinitely long line. But technically, half of infinity is still infinity.
The ray is equally long on one way and on the other way it stops or ends so it shorter. Over all though they both go to infinity so the are equal if u count both ways.
Yes, Because if you think hard about it you will find out that they both keep on going forever and will never stop so they will always be the same
It's like the theory of the universe being infinite. If you assume this to be true, and try to calculate the percentage of the space in the universe that we occupy, you couldn't really come up with any answer but 0. If the space is infinite, there is no "total" to use as a reference. In the same way, any two infinite lines are going to be of the same length, regardless of being a line or a ray. Neither has a terminating point for comparison.
there are different kinds of infinity. Read about the mathematician Cantor, and the concept of Aleph.
Yes. There's no biggest infinity.
A line or a halfray going to infiny, they are all going to infiny.
"some infinitys are bigger than others." = wrong!
You can compare infinity tending towards  or tending towards +, but you can't compare 2 infinities, they are considered as equal. There is halfray, but no halfinfinity!
A line or a halfray going to infiny, they are all going to infiny.
"some infinitys are bigger than others." = wrong!
You can compare infinity tending towards  or tending towards +, but you can't compare 2 infinities, they are considered as equal. There is halfray, but no halfinfinity!
Well, half of infinity is still infinity, but a smaller infinity. This is actually discussed in calculus.
Yes. It would both be the same. It would be the same because a ray is an infinite line. Also, a line is also an infinite line. Infinity stretches on forever, so they are equally the same length.
no. Both directions makes it longer than one
Here's a scenario I posted in a comment section: setting up a winding toy to start walking from one end point, and two winding toys back to back at another point to begin walking, all at the same time, and after however much time has passed of your choosing, measuring how far the one traveled vs. the line of the two when ending this ridiculous race of the winding toys. That would make for two line segments and not a ray and line though, at a measurable distance from one point to another.. so I would have to agree with many here on how neither beats the other one out a line extending infinitely both directions, and a ray extending infinitely in one direction to be equal in length in its concept.
No, that is not possible. The ray continues going on only in one direction, whereas the line goes on in both directions. The line's length is infinite, but the ray's length is infinite minus the space leftover, where the ray can not reach.
This is a difficult question to answer. technically, ray=line. But wait! double infinity.... that's strange!
Neither the ray nor the line truly has a length. Both are infinite quantities. When comparing infinities, you need to ask whether a onetoone mapping is possible or not. You can easily describe a onetoone mapping between a ray and a line, therefore the infinities are of the same size.
yes and no since a line is going on both ways and a ray is only one way but they both go on for ever
A few things to keep in mind ...
1) A Line, Line Segment, or Ray are tools _used to help make measurments of the real world_. They are not real themselves, you cannot pick up a Line, Line Segment, or Ray and put it in a bucket and walk around with it. In themselves they are theoretical, ultimately derived from real world measurments, and therefore use to assist in real world measurement....but still they exist only as an idea.
2) Measurement of the real world always have errors in them, they are ___neverever_ perfect. Perfect is for theory only.
3) *Finite* means having limits measurable, countable, calculable limts. All measurements are subject to error _and can be quantified_.
4) *Infinite* means something that is _not_ finite. Infinite _has no limits_, there is no definite number (quantification) that can be used to count and express the measurement of infinity *because infinity does not have the quality of being countable*. If it is not countable, it is not measurable, and not calculable. *No quantity can be assigned to infinity*. Keep in mind the use of the words _quality_ and _quantity_
5) If you consider the mathemetics of Limits in the context of calculus, it is defined as approaching a number, but not actually touching it, there is not definite quantity, only a relative approximation (even if it supersuper close, it is only an approximation).

Keeping the above in mind, when you ask if a ray and a line are equally long, the question itself is flawed.
Infinity does not have the quality of being measurable. *The use of the word _LONG_ is not applicable to the use of the word _INFINITE_ because there is no quantity to infinity*. You cannot measure the immeasurable.
This question has similar problems to answering "*Could you tell me the quantity of number values that exist between the number 1 and the number 2*" ? in that you are working with a continuum and trying to assign discrete values to it, and then trying to declare that you have stated all or most of them, at best you can only start from having none of them, and then have some of them.
Take some time to separate the ideas of point 1) and 2) above from points 3) and 4). There are differences between what it is, how you can describe it, and what you can do with it.

With respect to point 5) above, the question you posed would have calculus component to it if you asked to measure the distance travelled by an object moving away from a point in a straight line at a certain speed (Like a ray), as compared to the distance travelled by 2 objects moving in opposite directions from a point, each at a certain speed (Line a line). Can you see how a Ray, and Line are tools for measuring the real world?
Since the question was not constrained by a qualifier such as speed, it is incomplete and therefore also flawed. If it did have a speed component to some objects moving in some direction, you could get a length or distance answer for any time span from the starting point, whereever and whenever that starting point might be.
1) A Line, Line Segment, or Ray are tools _used to help make measurments of the real world_. They are not real themselves, you cannot pick up a Line, Line Segment, or Ray and put it in a bucket and walk around with it. In themselves they are theoretical, ultimately derived from real world measurments, and therefore use to assist in real world measurement....but still they exist only as an idea.
2) Measurement of the real world always have errors in them, they are ___neverever_ perfect. Perfect is for theory only.
3) *Finite* means having limits measurable, countable, calculable limts. All measurements are subject to error _and can be quantified_.
4) *Infinite* means something that is _not_ finite. Infinite _has no limits_, there is no definite number (quantification) that can be used to count and express the measurement of infinity *because infinity does not have the quality of being countable*. If it is not countable, it is not measurable, and not calculable. *No quantity can be assigned to infinity*. Keep in mind the use of the words _quality_ and _quantity_
5) If you consider the mathemetics of Limits in the context of calculus, it is defined as approaching a number, but not actually touching it, there is not definite quantity, only a relative approximation (even if it supersuper close, it is only an approximation).

Keeping the above in mind, when you ask if a ray and a line are equally long, the question itself is flawed.
Infinity does not have the quality of being measurable. *The use of the word _LONG_ is not applicable to the use of the word _INFINITE_ because there is no quantity to infinity*. You cannot measure the immeasurable.
This question has similar problems to answering "*Could you tell me the quantity of number values that exist between the number 1 and the number 2*" ? in that you are working with a continuum and trying to assign discrete values to it, and then trying to declare that you have stated all or most of them, at best you can only start from having none of them, and then have some of them.
Take some time to separate the ideas of point 1) and 2) above from points 3) and 4). There are differences between what it is, how you can describe it, and what you can do with it.

With respect to point 5) above, the question you posed would have calculus component to it if you asked to measure the distance travelled by an object moving away from a point in a straight line at a certain speed (Like a ray), as compared to the distance travelled by 2 objects moving in opposite directions from a point, each at a certain speed (Line a line). Can you see how a Ray, and Line are tools for measuring the real world?
Since the question was not constrained by a qualifier such as speed, it is incomplete and therefore also flawed. If it did have a speed component to some objects moving in some direction, you could get a length or distance answer for any time span from the starting point, whereever and whenever that starting point might be.
I say no, because a *ray* is going forever but in _one direction_ but for *line* it will go in _two ways forever_. So if you stop both at a certain point the ray will be two times shorter than the line because the line was going in two directions at once and the ray was going in one direction at once, so I would say no, the *ray* will not be as long as the *line*.
But if they never stop, it would be *infinite*, so there are _2 answers_, depending to the _*timings*_ (If they stop or go infinitely)._
P.S.The ones in *bold* are the one we are talking about.
P.S.S. So I say no, if it were yes than...
More
Example:
```
Line Segment
●●
Ray
>
Line
<>
```
That is my example.
So that us why I think *Lines* are longer than *Ray*, and this is the main reason, "_The *Lines* go in two different way(s) at the same time, but *Rays* go in one way(s)_".
P.S.S.S. Tell me if _you_ do not get it.
But if they never stop, it would be *infinite*, so there are _2 answers_, depending to the _*timings*_ (If they stop or go infinitely)._
P.S.The ones in *bold* are the one we are talking about.
P.S.S. So I say no, if it were yes than...
More
Example:
```
Line Segment
●●
Ray
>
Line
<>
```
That is my example.
So that us why I think *Lines* are longer than *Ray*, and this is the main reason, "_The *Lines* go in two different way(s) at the same time, but *Rays* go in one way(s)_".
P.S.S.S. Tell me if _you_ do not get it.
Yes the infinite line and ray would be the same because of how no matter what the lines go on for ever that is why on the end you make an arrow to show that it goes on forever. Also because that the degrees stay the same the small area at the bottom were the two lines meet do not change only the lines length. Now if you connect the lines and one is 20 cm long and another ray line is 5 cm long and you connect the lines the area will be different for both.
Well actually the line would be longer,because some infinity s are bigger than others.
Ex.:parts of whole numbers such as 1/8 1/3 1/4 and many others.
Ex.:parts of whole numbers such as 1/8 1/3 1/4 and many others.
well I guess it would be just as long on one side and not on the other
Alguns infinitos são maiores que outros...(John Green)
a ray ends at one point and continues the other side but if both were going the same speed the line would be doubling the size by both sides
just watch the video from 0:00 3:38 and learn stuff from it :3
but a ray has to end
a line can be as long as you want
a line can be as long as you want
yes they would both be equal
Well no because a ray spreads out infinitely in only one direction when a line spreads out in both directions therefore if you were to stop them from expanding the line would be about twice as long as the ray.
they are both infinite, so yes but infinity has no length so they couldn't be measured. even if a ray has only 1 side going to infinity, half of infinity is still infinity (or a quarter, or a eighth or even infinity for that matter)
i agree with the people who said that the ray only goes in one direction while the line goes in two opposite directions
no because a line is infinite in both directions but a ray is infinite in one direction
I believe so, since only line SEGMENTS stop at any piont of time.
No. Since a line goes on forever in both directions a ray only goes in one direction. It cannot be parallel.
There are different sets of infinity, so no. A ray is not as long as a line.
no and yes. no because a ray extends in only one direction while the other point is stationary.but a line extends endlessly in both directions .so a ray it will be 1/2 of a line.
yes is because both of them are infinite and no body can measure it.so we cannot say its exact distance.
yes is because both of them are infinite and no body can measure it.so we cannot say its exact distance.
You know, the line would be longer, because it goes into negative, and a ray does not! Well, if it starts negative, it does not go infinity down
Another way to think about it would be, if you cut an infinity sign in half, you get a circle, which is still infinite but in a different way.
Yes and no, because "equal" has little or no meaning when you're talking about infinity.
In my view (thinking of this as a philosophical question, rather than a mathematical one) infinite is the designation we give to things that are immeasurable. Infinite means "not finite" or "not measurable". Thus neither is knowingly bigger or smaller than the other because they have no measurable length or size. Both in essence have no distance, but the real distinction between the two is that a ray extends or "moves" (for lack of a better term) in one direction, while a line extends in two directions (i.e. movement to the right only as opposed to left and right simultaneously). Infinity is not truly a number, but a concept of something being limitless.
Think of infinity as a way to express an evergrowing number. Even if you take half of that number away, it is still evergrowing. Therefore, a ray and a line are the same length.
Take a look at this video. It talks about infinities and BIGGER infinities.
https://www.youtube.com/watch?v=elvOZm0d4H0
It talks about how some infinities are larger than others. For example, their are infinities in diagonals of fractions. It's hard to explain. Just check out the video.
https://www.youtube.com/watch?v=elvOZm0d4H0
It talks about how some infinities are larger than others. For example, their are infinities in diagonals of fractions. It's hard to explain. Just check out the video.
I think that both the ray and the line are the same length. If you think about it, there doesn't necessarily need to be negative and positive numbers denoting every single point on the line and ray. That case would only be on a plane. If you have any more questions, please reply below. Hope this helps!
Infinity and infinity = infinity no matter what.... so what Gabe said is right they cannot be diffrent lenghts even tho one starts and one is twice the size... (This part refers to a movie skip if you haven't seen it Unless you wanna under stand it better>) Think of it as in transformers... That big cube... it was still the same power even when it was bigger or smaller, that is the same thing with infinity... (END OF MOVIE REFERENCE) As in the example Its the smaller or bigger thing such as ray and line that is equal. Even tho they are diffrent numbers that don't come out right... In infinity multiplicationadditionsubtractiondevision with any number would still come out to infinity so infinity would never ever not be equal to itself.
Like nickspoon said, it doesn't matter if it is a ray or a line because infinity is the concept of things that never end. so basically, they would be the same never ending length.
the line would be longer. as some one said ealier set theory.
if you were to count 1 , 2, 3 , 4 ....
and someone else counted 1 , 1.5 ,2, 2.5 ,3 , 3.5 ...
the second one would have more
if you were to count 1 , 2, 3 , 4 ....
and someone else counted 1 , 1.5 ,2, 2.5 ,3 , 3.5 ...
the second one would have more
I believe that you just blew my mind...
No because a ray only stretches in one way a line stretches in both.
I guess no because a line doesn't have an end or starting point and a ray does so the line must be longer
No because an infinite line is going to go forever in both directions and a infinite ray will go forever in only one direction.
No because an infinite line is going on forever in two directions, but a infinite ray is going on forever in one direction
An infinite ray is one half of an infinite line. So that means an infinite line isn't equal to an infinite ray.
my guess is that the line would be longer, because while the ray would go infinite in one direction, the line would go infinite in both directions making the line longer. that is a really good question.
No because infinite line has no starting or ending point where an infinite ray has an starting point.
No because a line is different from a ray
no, because a ray only expands in one directions unlike a line which expands in both directions.
You have just entered the world of Calculus and Limits! What is greater....x^3 or x^9 as x approaches infinity?
a ray extends in only 1 direction, but a line extends in both directions. So an infinite ray would be half of an infinite line because a ray is one direction, or half of a line
It's actually simple 1 DOES NOT = 1/2
here:
1≠ 1/2
here:
1≠ 1/2
What is the difference of a ray line segment and a line?
A line segment connects two points and stops at those two points.
A ray starts at a point and continues forever in one direction.
A line continues forever in both directions.
A ray starts at a point and continues forever in one direction.
A line continues forever in both directions.
Yes. It's a tricky concept because it feels like an infinitely long ray is only half as long as an infinitely long line. But technically, half of infinity is still infinity.
A line segment connects two points and stops at those two points.
A line segment has 2 end points, and 0 arrows.
A ray starts at a point and continues forever in one direction.
A ray has 1 endpoint, and 1 arrow.
A line continues forever in both directions.
A line has 2 arrows, and 0 endpoints.
A line segment has 2 end points, and 0 arrows.
A ray starts at a point and continues forever in one direction.
A ray has 1 endpoint, and 1 arrow.
A line continues forever in both directions.
A line has 2 arrows, and 0 endpoints.
Wow very good info!
A line segment has two end points however a ray has one end point and the other side goes on forever think of it as the suns rays and a line continues in both directions forever with no endpoints! Hope this helps! :)
A ray has one starting point, then goes on forever, in one way or the other, a line has neither a starting point or an ending point, going on forever, and a line segment does have a starting point and an ending point, which connect to make a line segment.
if you watched the video you would understand
A line segment has two end points,ray has one end pint while line has no any end point
in 2:48 it answers it
Answer this question...
Answer this question...
A line segment is a line that has 2 endpoints. 0:40 and a line goes on forever. 1:05
A ray starts at a point and continues through a second point to infinity.
A ray has a starting point but goes in one direction with no end. A line segment has a starting point and an ending point. A line has neither has a starting or an ending point and goes in both directions.
basically, the difference lies in the start and end points.
a line segment has BOTH a starting point and an end point.
a ray has ONLY a starting point.
a line has NEITHER a starting nor an end point
a line segment has BOTH a starting point and an end point.
a ray has ONLY a starting point.
a line has NEITHER a starting nor an end point
I Agree with Catherine My Vote
A ray starts at a point and then it just keeps going a line has no points and it does not stop and a line has two points a starting point and a ending point
Well, A ray has a starting point but it keeps going on forever...But a Line has neither a starting or a ending pointit keeps going on forever from both sides.
A ray has one ending point, whereas a line continues forever.
A ray line segment is a line that has a darting point and a line segment (part of a line) in middle however a line has no points and goes on forever on both sides
A ray line segment has a starting point and goes on forever. A line segment has a starting point and an ending point. A line goes on forever on both directions.
Is the question: what do you get when you subtract a ray from a line?
Wouldn't that leave another ray?
But would you know the starting point of the result ray?
If you don't know the starting point of a ray, is it still a ray?
This is getting into set theory: rays and lines are infinite sets of points.
Wouldn't that leave another ray?
But would you know the starting point of the result ray?
If you don't know the starting point of a ray, is it still a ray?
This is getting into set theory: rays and lines are infinite sets of points.
So then what is the point of infinite ray and infinite line?
A ray begins at a point and then continues on in one direction like the rays of the sun. An infinite line goes off in both directions. It has no beginning and no ending.... much like a highway has many points you can stop along the way but seems to continue on and on in both directions.
a ray has one vertex but the line doesnt have a vertex from the both sides it keeps on going from each side.
ome oh waneo my omg
;)
;)
To get an geometric figur because geometry is made of points,line segments and strait lines
An infinite ray has a starting point, goes off in one direction with no end. An infinite line has no starting or ending point and goes in two directions.
considering that, as someone said, half of infinity is still infinity, you would never be able to get to the end represented as an arrow whereas it would actually be possibly to reach the point represented as a dot
A ray is limited to one direction, and goes on infinitely in that certain direction. On the other hand, a line is not limited to anything concerning the directions on a 2D plane. (You can only go left, right, up, and down on a 2D plane). The point is very controversial. I would personally say that this is just pure geometry. It doesn't need to be practical. We do this just for the sake of understanding. For example, there isn't anything that actually goes on forever in any direction in real life. That is, unless it is light.
A line doesn't have a point but a ray has a starting point
An infinite line has no start or nor end. a ray has a start, but goes on forever.
a ray doesn't have a point,it has a thing that looks like this on the end: > . a line doesn't have a point too,only a line segment
the main difference between the two is that a ray actually has a starting point, though it doesn't necessarily have an end point, whereas a line has neither a starting nor and end point
What is a segment?
A segment(when talking about a line) is only part of a line. Like he said, a line goes on forever but a line segment doesn't. ♥
A line segment is a line in which it has a starting point and an ending point.
Have you watched the video? Let us know which part you didn't understand.
Some thing that is divided into two parts.
Yes, even in everyday language a segment is just a "part of".
a segment directly means a part
so a line segment is a prat of a line
so a line segment is a prat of a line
a line segment is part of a line
He explains it in this video: https://www.khanacademy.org/math/geometry/segmentsandangles/intro_euclid/v/languageandnotationofbasicgeometry
Basically, a segment is a line with two endpoints. It doesn't go on forever like a line, and a segment can be part of an infinite line.
Basically, a segment is a line with two endpoints. It doesn't go on forever like a line, and a segment can be part of an infinite line.
You mean a line segment a line segment is a line that has a starting point and an ending point.
A segment is nothing but the part of a line.a line extends infinetly whereas a line segment ends at its end points & has finite length.
A part of a line
A line segment is two points on a line on each side.
look im not a girl! and i doin this for fun ! plus i am kurtzed1, and i ahead of my grade!!!!!
What if the ray was coming from both sides like this:
<ooo>
Would this be a ray or a line?
<ooo>
Would this be a ray or a line?
If it does not start with a point, then it is not a ray. it is a line.
Ray o>
Line <>
Ray o>
Line <>
That would be a line.
A Ray would never come from both sides so yes it is a line.
It depends on how you look at it. If these are just collinear points, then yes, it is a line. But if the middle point is an origin point (which is what I think you meant) Then it would be two rays.
That is a line because it has points in the middle and it has 2 arrows. (> ray) (<oo> line)
that isn't a ray. .> ray
It's a line. <> line
It's a line. <> line
Set of infinite points which they are collinear
can a line also be a ray?
Lines cannot be rays.
Line: Extends forever in two directions
Ray: Extends forever in one direction and has one endpoint
Line Segment: Has two endpoints and doesn't extend forever
Line: Extends forever in two directions
Ray: Extends forever in one direction and has one endpoint
Line Segment: Has two endpoints and doesn't extend forever
No because a line extends in both directions but a ray extends in only one direction
We'll yes it can because lines and rays both have end points and go strait
blah people you guys will become millionaires
Would time be described as a line or a ray?
Or can it even be described that way?
Are there similar properties to ideas with more dimensions?
Or can it even be described that way?
Are there similar properties to ideas with more dimensions?
That is an interesting thought. To answer these question we would need to know if time had a start as well if time will have an end.
Assuming that time can be described this way, I believe that time could be represented as a ray. I'm assuming that time started 13.7 billion years ago when the big bang occurred. I am also assuming that the universe will never end which is the prevailing theory as of now, but some scientist disagree and argue that the universe could have an end.
Things can get very confusing when you take into effect the theory of relativity which states that time is not the same for everyone. If someone is moving then time is passing by slower than someone not moving! This means if i move for a little and then stand still, my experience of time will be completely different from someone standing still the entire time! (The difference in time would only be recognizable when moving at a large fraction of the speed of light which is about 300,000,000 meters per second or 186,000 miles per second so if I move the time dilation will be so small no one will recognize it but it will have occurred!) This means if I drew a time ray mine would be different than the other person not moving!
Things get very interesting if we consider extra dimensions. We live in a universe with 3 spatial dimensions and 1 time dimension. Since time is a dimension what if there was multiple time dimensions in another universe? If time had 2 dimensions time would have to be represented as an plane! This place could have an infinite edge and an noninfinite edge! What if time was 3 dimensional! Now I'm all excited! It could be any object that is three dimensional. We could have a universe with its time, if graphed, to look like anything.
Just remember Leo that even the most simplest of question can have the most mindblowing answers.
”I don't know anything, but I do know that everything is interesting if you go into it deeply enough.”
Richard Feynman
Assuming that time can be described this way, I believe that time could be represented as a ray. I'm assuming that time started 13.7 billion years ago when the big bang occurred. I am also assuming that the universe will never end which is the prevailing theory as of now, but some scientist disagree and argue that the universe could have an end.
Things can get very confusing when you take into effect the theory of relativity which states that time is not the same for everyone. If someone is moving then time is passing by slower than someone not moving! This means if i move for a little and then stand still, my experience of time will be completely different from someone standing still the entire time! (The difference in time would only be recognizable when moving at a large fraction of the speed of light which is about 300,000,000 meters per second or 186,000 miles per second so if I move the time dilation will be so small no one will recognize it but it will have occurred!) This means if I drew a time ray mine would be different than the other person not moving!
Things get very interesting if we consider extra dimensions. We live in a universe with 3 spatial dimensions and 1 time dimension. Since time is a dimension what if there was multiple time dimensions in another universe? If time had 2 dimensions time would have to be represented as an plane! This place could have an infinite edge and an noninfinite edge! What if time was 3 dimensional! Now I'm all excited! It could be any object that is three dimensional. We could have a universe with its time, if graphed, to look like anything.
Just remember Leo that even the most simplest of question can have the most mindblowing answers.
”I don't know anything, but I do know that everything is interesting if you go into it deeply enough.”
Richard Feynman
Time goes the same no mater what exept using Einstienes thiery of relativity traveling at the speed of light (you can't go faster) or in space
what are skew lines
In other words, you can only have skew lines in 3 or more dimensions, because in 2D plane geometry, lines are either parallel or intersecting, but not both and not neither.
Skew lines are lines that do not intersect but are not parallel.
They are not on the same level or plane for this to happen like one line goes over another like a bridge over a road but it is neither intersecting nor parallel.
They are not on the same level or plane for this to happen like one line goes over another like a bridge over a road but it is neither intersecting nor parallel.
If it does not start with a point, then it is not a ray. it is a line.
Ray o>
Line <>
Ray o>
Line <>
They are not parallel and they never meet
do rays relate to line segments?
it does, because you can the the infinite line in half
I don't think so! Rays only have one end point, line segments have two end points in which do not go in either direction, and Rays on the other hand go on forever in only one direction because Rays only have one end point!
Rays do relate with line segments. Line segments have at two points in which go on forever in both directions. Rays also have two points, but one point goes forever in a direction and the other point has an endpoint and doesn't extend forever.
If you start with a line segment, say segment AB, you can define ray AB (which has an endpoint at point A) as the union of segment AB and all points that are beyond point B and collinear with segment AB.
what is the difference between a ray segment and a line?
A ray has one endpoint and travels in one direction, while a line is the total opposite of a line segment, having no endpoints and travelling in 2 directions, going into infinity.
A ray segment is when you have a defined starting and you go off in any direction and then have a defined stopping point.A line has no defined starting and no defined ending,so it goes on forever.I hope this helps!
A ray has a point on one end of the line, but on the other end there is no ending. It continues forever in one direction. A segment has one end point on one side, and one on the other. In other words, it doesn't extend forever in any direction. A line has no end points. The line continues forever in both directions. Hope this helps!
a ray goes on in one direction,a line never stops, and a line segment has two ends
A ray segment has somewhere to stop. A line goes in both directions and does not end.
I think so because a ray comes with an end point
A Ray goes on forever in one direction, a line goes on forever in both
A line does not end.A ray segment has a stopping point
at 1:49 in the video, it said that a ray had a well defined starting point? What did they mean? Did they mean the little arrow on the end?
the little arrow tells us that it can extend in that direction where that arrow points to infinity. However, the dot/ point on the opposite end of the ray (or on the opposite of the arrow ) indicates the starting point. It is fixed and cannot be moved/ extended.
A line is a series of points which keep growing from both ends. A line segment is a portion of line with two end points. A ray is a line which has got one end point. The open end point is infinite.
Thanks
Thanks
What is an exact position called ??
At 1:34, what does Sal mean by "abstract notions?"
*Abstract Notions*: Things that different/exotic, and don't usually appear in everyday life. Abstract notions are mainly used in math.
In this video, the abstract notion is the line: it continues forever
Hope that helps!
In this video, the abstract notion is the line: it continues forever
Hope that helps!
Can a ray be named after a single point(origin) or is it necessary that it should pass through another point, also if a ray is passing through three points or more
for example : a ray starting at point A passing through point B further through point C and the ray is named as Ray AB can it also be called Ray BC?
for example : a ray starting at point A passing through point B further through point C and the ray is named as Ray AB can it also be called Ray BC?
A ray needs to have two points. Either name is acceptable.
Both seem okay, since a ray needs an end point and an arrow on the other end. Both fit that description.
if a a ray is infinte but with a starting point does it never come back onto itself? essntialy then turning itself into a line?
this concept is more the fact that it would continuously move through infinitesimal space and time and is a universal concept. you don't see the beginning or end. a ray is a point in witch a line is separated based on intended direction. because spacetime is a three dimensional plane a ray can travel anywhere on this plane as long as it doesn't curve
No because as he said in the video at 2:57 and other parts it goes IN ONE DIRECTION. Imagine a flat infinity.
Well that cant happen because a ray goes on in one direction for ever, and a line goes on for 2 directions forever.
A ray is straight, so it will never come back to itself. However, it is not a line. A line "expands" forever both directions ( <> ), but a ray only "expands" in one direction ( •> ). I hope this explanation helps.
Well, I sort of disagree. It's exactly the fact that a ray is straight that means it WILL come back to itself, since spacetime is 3dimensional.
At 2:33 they say that the figure is a line. But two endpoints are given, so it doesn't make sense for it to be a line and not a line segment.
It's useful to focus on the arrows  at both ends  that tells us, "YES" it can be a line.
(In the video around 1:00 minute, when Sal sketched a line... I think he should sketch two points along the line, however, he was busy emphasizing those arrows at each end to show it is a line.)
It is good that you saw that it seems to represent a line segment, because the two points there, show a segment within the line. (If the question was, can this represent a LINE SEGMENT? it would be right to say, YES.)
A LINE is defined by two points (where any point has a location) and the line does NOT STOP at either point, so two "arrows" in the sketch always means "this is a line."
Two points A and C and the sketch extends with lines and arrows away from both of two points, can correctly be identified as line segment AC, ray AC, ray CA, and line AC (or line CA).
(In the video around 1:00 minute, when Sal sketched a line... I think he should sketch two points along the line, however, he was busy emphasizing those arrows at each end to show it is a line.)
It is good that you saw that it seems to represent a line segment, because the two points there, show a segment within the line. (If the question was, can this represent a LINE SEGMENT? it would be right to say, YES.)
A LINE is defined by two points (where any point has a location) and the line does NOT STOP at either point, so two "arrows" in the sketch always means "this is a line."
Two points A and C and the sketch extends with lines and arrows away from both of two points, can correctly be identified as line segment AC, ray AC, ray CA, and line AC (or line CA).
how can you remember the segments more easily
A segment is not infinite and has 2 endpoints.
If you imagine a line first, you should imagine a line with an arrow on both ends, and a line extends forever in both directions. A ray should look like a line, but instead one end has a point to end the line from extending in that direction. A ray extends in one direction. A line segment, has two endpoints, one on each end, and a segment never continues on in any direction. If you can imagine this, you can slowly see the differences between a line, a ray, and a segment. This may help you understand. :)
If there is only one point defined in a ray, could you define it? If so, how?
A ●────────>
A ●────────>
You can't with just one point. You would need a second point somewhere on the way to show what direction it is going in.
Does it mean you can't draw a ray and line?
And why people usually call line segment as line?
And why people usually call line segment as line?
Well, you can't exactly draw one, but you can indicate them by putting arrow heads.
I think a lot of people grow up using the term line, and can't be bothered saying line segment.
I think a lot of people grow up using the term line, and can't be bothered saying line segment.
How can a infinite line be equally to a infinite ray if the line goes on on both ends and the ray goes on on one end?
A line can go on infinitely in both directions. A ray can only go infinitely in one direction because it starts from 1 point. Typically, the lines you see in school at this time are actually line segments. Line segments have 2 endpoints; 1 on each end.
can a line segment be infinte cause you could place the two points anywhere? That's my question
an infinite line is called a line or ray
So what is the difference between a ray and a line?
A line goes on forever in both directions. A ray has a starting point, then goes on forever in one direction, kind of like a flashlight beam.
Nice outcome on the comparision
a ray has a starting point but no ending point ( which means it end will just keep going on and on), and a line has no starting or ending point and just goes on forever in both directions.
Hope you found this helpful! :):)
Hope you found this helpful! :):)
So Is the universe a ray,line or line segment?
The universe is a plane. Like a plane, it goes on forever and ever.
The universe would be a 3 dimensional plane, for an easier way of defining.
A universe is the universe.
Is there such thing as a acute line segment
No, "acute" only applies to angles that are smaller than 90 degrees.
Angles are related to line segments because, two segments, that share one point, are the formation of an angle.
Does a line have to have arrows at the end?
Yes it does. Both ends in fact. This is so to distinguish it from a ray, or a segment.
no:) as long as you don't put endpoints on it, you can leave the sides open.
__________________
^see that still counts as a line cause it has no endpoints.
__________________
^see that still counts as a line cause it has no endpoints.
No the line doesn't because you could draw a straight line. Nice question though.
The line with the arrows is just a representation of a line. A line is a geometric shape that has length but no width. The arrow on a line indicates that it goes on in that direction without end while the dot at the end of a line segment or ray indicates the end point. Neither the dot nor the arrow are part of the line. They are just symbols showing the continuing or ending of the line similar to the way a stop sign or a sign saying "10 miles to next gas" are not part of a road but symbols indicating the end or continuing of the road.
would the steps to finding the answer to these problems, always be the same?
there are lots of ways to solve problems in math. i like to use one same way each time so i dont get mixed up :)
nowadays why do people call line segments ,lines
In a conversation outside a math classroom, "line" is descriptive enough, But math users like to be precise.
Even though I think I know the answer,why can't an infinite line and an infinite ray be the same?
Mathematical reality and physical reality are often similar, but are not necessarily identical, so from a mathematical point of view... no.
Consider a ray AC which starts at point A and continues in the direction of C forever. Most simply put, ray AC ends (at A) and line AC does not, so any point collinear with AC but on the other side of A from C is on line AC but not on the ray AC, so ray AC and line AC cannot be congruent.
Consider a ray AC which starts at point A and continues in the direction of C forever. Most simply put, ray AC ends (at A) and line AC does not, so any point collinear with AC but on the other side of A from C is on line AC but not on the ray AC, so ray AC and line AC cannot be congruent.
Why would there be line segments inside a line? I thought It was only part of a line and it wouldn't be inside
If there are four points on a line, there are nine different segments. Think of each little space between the points as a segment by itself. All the other segments create other segments, and each single segment can be used as many times as the patterns require. It's the same basic principle as those "Jim has three shirts and three pairs of pants. How many combinations are there?' questions.
Hope this helps and I didn't confuse you!
Hope this helps and I didn't confuse you!
What are the similarities and differences between a line and a line segment?
A line segment is a portion of a line that has a finite length.
No a line segment ends on both sides. A line goes on forever.
What is the easiest way to remember the difference between line segments and lines?
a line segment has a dot on each end and a line has an arrow on each end . also a line goes forever in both directions .
Line segments have dots on each end of the segment where as lines have arrows on each end.
how do you get to the practice based on this video
Here's the practice section for that video:
https://www.khanacademy.org/math/geometry/intro_euclid/e/recognizing_rays_lines_and_line_segments
https://www.khanacademy.org/math/geometry/intro_euclid/e/recognizing_rays_lines_and_line_segments
Sal Just a side note, if you play the video," recognizing lines"in 4th grade, and add captions, it talks about beer and counting Koreans, I think the computer takes what your saying and mishears it.
why did they come up with signs to represent rays, line segments, and lines?
Mathematics is a language with its own set of symbols. There are many symbols that simply make it shorter to write than to have to write out the words when designing proofs. Rays are used in the definition of angles and we have to have a concept of lines before we can take only a part of it (a line segment).
Can someone make this a little more simple please?
A line goes on forever in both directions.
A ray starts from a point and continues forever in one direction. In the same way, the sun's rays start from the sun and continue forever in one direction.
A line segment is just a part of a line. It has a clear starting point and a clear ending point.
Hope that simplifies it
A ray starts from a point and continues forever in one direction. In the same way, the sun's rays start from the sun and continue forever in one direction.
A line segment is just a part of a line. It has a clear starting point and a clear ending point.
Hope that simplifies it
Line = is an undefined segment which has no starting point nor ending point
Line segment = a segment defined by a clear starting and ending point
Ray = a segment that has a defined starting point but an undefined ending point
Line segment = a segment defined by a clear starting and ending point
Ray = a segment that has a defined starting point but an undefined ending point
what's the difference between an infinite ray and a ray?
No difference I can think of... a ray starts at a point and continues in a direction forever. All rays are infinitely long.
wouldnt two rays be equally long
Yes, a ray is infinitely long, so even if you traveled down a ray thousands or millions of miles, the remaining part would still be infinitely long. Also the line, which extends in both directions, is also infinitely long, the same length.
Years ago I heard a puzzle about a hotel with an infinite number of rooms and an infinite number of people, one in each room. Then another infinite number of people came wanting rooms. What should the hotel manager do? Well he could move the infinite number of people already in the hotel into just the odd number rooms since there are an infinite number of odd numbered rooms. Then he would have an infinite number of even numbered rooms to put the new people in.
The same thing could be done to show that a line is equally as long as a ray. If you look at the line as a number line with a point marked as the zero mark, you could take each positive foot long line segment and move it to the odd numbered segment positions so the segment that started at zero and went to one would stay where it was, and the segment that started at one and went to two would move to the space from two to three and so on. Then the segments on the negative ray of the line could be moved to the even positive positions so the segment that went from zero to negative one would be moved to the position from positive one to two, and the segment that went from negative one to negative two could be moved to the position between positive two and positive three, and so on. This would map the line segments from both the positive ray and the negative ray of the line to just the segments of the positive ray with no overlap and no gaps extending on to infinity and showing that the line, consisting of a ray in both directions, and the ray, extending in only one direction, are equal in length.
Years ago I heard a puzzle about a hotel with an infinite number of rooms and an infinite number of people, one in each room. Then another infinite number of people came wanting rooms. What should the hotel manager do? Well he could move the infinite number of people already in the hotel into just the odd number rooms since there are an infinite number of odd numbered rooms. Then he would have an infinite number of even numbered rooms to put the new people in.
The same thing could be done to show that a line is equally as long as a ray. If you look at the line as a number line with a point marked as the zero mark, you could take each positive foot long line segment and move it to the odd numbered segment positions so the segment that started at zero and went to one would stay where it was, and the segment that started at one and went to two would move to the space from two to three and so on. Then the segments on the negative ray of the line could be moved to the even positive positions so the segment that went from zero to negative one would be moved to the position from positive one to two, and the segment that went from negative one to negative two could be moved to the position between positive two and positive three, and so on. This would map the line segments from both the positive ray and the negative ray of the line to just the segments of the positive ray with no overlap and no gaps extending on to infinity and showing that the line, consisting of a ray in both directions, and the ray, extending in only one direction, are equal in length.
YES! They would both be of infinite length. Keep up the deep thoughts, they're good for your brain. ;)
What is the difference between a line and line segment? (Curious)
A line goes out to infinity in both directions. A line segment ends and has a finite length.
A line segment is a piece of a line with a starting point and a stopping point.
A line will just keep going in either direction (usually has arrows on the ends).
A line will just keep going in either direction (usually has arrows on the ends).
What If I were to draw a line around the circumference of a sphere for example, the equator. Do I have a line or a line segment?
You have a 360 degree arc.
A line is by definition straight, no curving around a circle/sphere.
Neither, a line the way we are learning here is straight and not to be confused with the way someone would speak of a line in art. The circumference of a sphere would be a circle, which is not straight, and a part of that circle would be an arc, not a line segment.
would an infinite line and an infinite ray be equally long?
Infinity is infinity. So yes, they would be equally long. Imagine that a ray has a length of infinity. Then imagine a line that has a length of infinity. In theory, they both have lengths of infinity and the line cannot be longer than the ray. Now, if 'infinity' were a normal number, then the line would be twice as long as the ray. But, as I said, infinity is infinity, so in both cases they are extending forever. Hope this helps!
P.S.: This is fun to think about, isn't it?!
P.S.: This is fun to think about, isn't it?!
No. A line will always be longer than a ray. A ray has a point that starts it. A line keeps going either way! :) hope this helps! :)
April is correct. Aisha, infinity is infinite, and half of infinite is still infinite. The two are equally long.
infinite means that it does not end witch means that you can not tellhow long it is
If a ray went infinitely around the Earth, would the end of the ray that keeps going meet up with the other end and become a line?
What is described in the question above, is a curve, and it is not in a single direction like a ray has to be in a single direction. A ray can not curve around Earth, a ray can start at Earth and extend to space. Curves, are never rays, or lines, in geometry definitions. A ray can never meet the start point. Also, a line can not be defined as in the question, as something that goes around and meets the starting point, a line can only go infinitely along in directions away from one point, never meeting up "end to end."
Your question is so important because it hints that you are thinking about the idea of a "curved ray" (or "curved line") and you will have a better time with calculus, because you are thinking about "curved lines".
To be certain about solving geometry problems it's important to be certain that a ray is described by an startpoint and a single direction, not a curve. A general example is, think of the ray of light (like from a laser) it's got a start point, and goes in a single direction  a ray of light.
(A "curved line" is  mathematically  made of teeny segments connected point to point. Here you are entering into calculus, where the teeny segments get cut up teenier and teenier.)
Hope that helps.
Your question is so important because it hints that you are thinking about the idea of a "curved ray" (or "curved line") and you will have a better time with calculus, because you are thinking about "curved lines".
To be certain about solving geometry problems it's important to be certain that a ray is described by an startpoint and a single direction, not a curve. A general example is, think of the ray of light (like from a laser) it's got a start point, and goes in a single direction  a ray of light.
(A "curved line" is  mathematically  made of teeny segments connected point to point. Here you are entering into calculus, where the teeny segments get cut up teenier and teenier.)
Hope that helps.
Meet up with other line.
how much time does it take to make one of your supreme videos
What happens if you tell the difference?
what does collinear mean?
Points that are in order to form a line
Points that lie on the same line are collinear...
•A•BC• Points A,B,and C are collinear...
•A•BC• Points A,B,and C are collinear...
lie on the same line
Are lines and rays associated?
lines and rays are not associated