If you're seeing this message, it means we're having trouble loading external resources for Khan Academy.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Watch the entire video

Lines, line segments, and rays

Difference between lines, line segments, and rays

Lines, line segments, and rays

Discussion and questions for this video
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.
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.
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 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. ♥
What if the ray was coming from both sides like this:
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- <----------->
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
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?
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 non-infinite 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 mind-blowing answers.

”I don't know anything, but I do know that everything is interesting if you go into it deeply enough.”
-Richard Feynman
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.
it does, because you can the the infinite line in half
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.
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.
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!
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?
A ray needs to have two points. Either name is acceptable.
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 space-time is a three dimensional plane a ray can travel anywhere on this plane as long as it doesn't curve
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).
how can you remember the segments more easily
A segment is not infinite and has 2 endpoints.
If there is only one point defined in a ray, could you define it? If so, how?
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?
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.
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.
So Is the universe a ray,line or line segment?
The universe is a plane. Like a plane, it goes on forever and ever.
Is there such thing as a acute line segment
No, "acute" only applies to angles that are smaller than 90 degrees.
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.
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.
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!
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.
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 .
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
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.
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.
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.
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?!
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 start-point 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.
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
Are lines and rays associated?
lines and rays are not associated
1 Vote
Comment Flag