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### Course: 6th grade (Illustrative Mathematics) > Unit 7

Lesson 15: Lesson 15: Shapes on a coordinate plane- Points on the coordinate plane examples
- Drawing polygons with coordinates
- Area of a parallelogram on the coordinate plane
- Area and perimeter on the coordinate plane
- Coordinates of a missing vertex
- Example of shapes on a coordinate plane
- Dimensions of a rectangle from coordinates
- Quadrilateral problems on the coordinate plane
- Quadrilateral problems on the coordinate plane
- Parallelogram on the coordinate plane

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# Parallelogram on the coordinate plane

Remember our discussion of the coordinate plane? Sure you do! Let's graph the given coordinates of three of the polygon vertices, and find where the 4th vertex is. Created by Sal Khan.

## Want to join the conversation?

- what would a line with a negative length look like?(14 votes)
- Well a line will always be positive because it's straight with no curves but you can say that the points can be negative so in conclusion it'll just look like any other line(20 votes)

- I dont get1:25. can someone help?(11 votes)
- This is just instructions from the math problem saying that Sal has to make both lines the same length. I hope that's what you were asking for, and if it isn't, please be more specific.(18 votes)

- I don't get it please help.(15 votes)
- he found the length of the top line because the top is the same length as the bottom in parallelograms.(4 votes)

- if anyone has a problem remembering horizontal and vertical, here is a simple trick. Horizontal comes from the line in the horizon of the sun, sea, ocean, etc. I hope this helped :)(13 votes)
- I've heard that a polygon cannot have curved edges or incomplete sides, so would a circle not be considered a polygon? I mean it is a shape, and all shapes are polygons, right?(8 votes)
- Not all shapes are polygons, and circles have curved sides so they are not polygons.(9 votes)

- If we use the distance formula to solve for this, without knowing that it has to be a parallelogram, than we can get many points that make a polygon ABCD but the polygon is not a parallelogram! Then why does it have to be a parallelogram?(7 votes)
- This problem does not say to use the distance formula. Yes, I know this sounds like the problem is some dictator, but, while we're doing it, it is a dictator of sorts.(7 votes)

- why not just count the units?(6 votes)
- You definitely can just count the units. However, if you're dealing with units that are farther apart....... maybe with distances of 100 or more in between, then counting would become a long and tedious process.

You could also just take the absolute value of the x-coordinates since the y-coordinates are the same to find the distance in between.

Ex. | -1.5 - 4.5 | = | -6 | = 6(6 votes)

- This is soooooo HARD(7 votes)
- Sup CalebB, It can be a little hard, but you can get through it! Try and look up other videos or use AI tutoring (That can help greatly). Most importantly, keep trying. Hope this helps! ✌︎ ♡ ☺︎ ☆(3 votes)

- Does anybody else have a problem in using "Drawing polygons with coordinates" For me it is not might user friend. I know the answer but cannot get the hang of plotting it on screen.(7 votes)
- Yes I do sometimes, but if you keep practicing plotting different ones out, you start to get better at drawing them out correctly. Hopefully that helps!(3 votes)

- how big is the biggest coordinate plane (in Numbers) in the world?(5 votes)
- The biggest coordinate plane in the world is infinitely long in EVERY direction. On a lot of apps you can keep zooming out forever.(5 votes)

## Video transcript

- [Instructor] You are
graphing Polygon ABCD in the coordinate plane. The length of segment AB must
be the same as the length of segment DC, and both segments
are horizontal segments. The following are three of
the vertices of the polygon. So vertex A is at the point one comma one. So one comma one, it
puts us right over there. That is vertex A. Vertex C is at the point 4.5 comma four. So 4.5 along the horizontal axis, comma four, comma four. So we go all the way,
we go all the way up to, all the way up to four. So that right over there is point C. Point D is that negative 1.5 comma four, so negative 1.5 along the horizontal, or I guess we know the
x-axis, we could say. Negative 1.5 comma four, so four along the vertical or the y-axis. So we go right up, go right over there. That's close enough. So that of course is our y-axis. This is point D. And we need to figure out
what are the coordinates of point B if B must be in Quadrant 1. And they tell us that the distance from A to B must be the same as the
length of segment D to C, and both are horizontal. So let's draw what we know to draw. So DC, segment DC, segment DC is this
segment right over here, is this segment right over here. And we see it's horizontal. Both of the vertical coordinates are four at both vertex D and vertex C. So both of the vertical
coordinates are four. Now what is the length of this? Because we're gonna have to
construct another segment that has the same length. Well, along the horizontal direction, we went from negative 1.5 to 4.5. So how far did we go? Well, to go from negative 1.5 to zero, you go 1.5 and then you
have to go another 4.5. So this is going to be 4.5 plus 1.5, which is equal to four plus
one is 5, .5 plus .5 is one. So five plus one is six. So this distance right over
here is six of our units. Another way of thinking about it, and actually let me put
the coordinates in here just so it becomes a little bit clearer. This was the point four point... Lemme do that in something easier to see. This right over here is
the point 4.5 comma four. And this right over here is the point negative 1.5 comma four. And so another way of
thinking about this distance is you could take the end point, and we're really thinking
about the distance just along, it's a horizontal line, so
the y value does not change. It doesn't change in
the vertical direction, only the horizontal. So you really wanna say, well, how far is, if you start at negative 1.5 and you get to 4.5, how far have you gone? So you can just take your
end point, your end value, your end horizontal
value, your end x value, and from that you can subtract
your starting x value. So you subtract negative 1.5. And this of course is equal
to 4.5 plus positive 1.5, which once again is equal to six. So, fair enough, and lemme
draw some of the rest of the polygon just so that
we see it is indeed a polygon. So we have this side right over here, and it looks like it's
gonna be a parallelogram. So we have this side right over here and we have to replace point B. And point B is gonna
be someplace out here. It's going to have the same vertical value or the same y value is point A. So its y-coordinate is going to be one. So point B is going to be
out here someplace, point, lemme just in a new color. So point point B. I haven't used this orange yet. Actually, I have used the orange yet. I haven't used the yellow. No, I've used the yellow. Let's see, I haven't used this green. Point B is going to be someplace out here. So point B is gonna be someplace out here. We already know what its y-coordinate is. It's a horizontal line, so it's gonna have to have
the same exact y-coordinate as point A. Point A's y-coordinate was one. So this is going to have to
have a y-coordinate of one. Now the big question is, what is its x-coordinate going to be? Well, it's going to have to be... Let me do that in a different color. It's going to have to be
whatever A's x-coordinate was. It's gonna have to be
whatever A's x-coordinate was. And we see that A's x-coordinate was one. It's gonna have to be that plus six 'cause we're gonna move the same distance in the horizontal direction. This thing has to be six. So if we start at one, we
add six, we get to seven. So what are the coordinates of point B? And especially if point
B must be in Quadrant 1. And notice we are
definitely in Quadrant 1. This is Quadrant 1, this is Quadrant 2, this is Quadrant 3,
and this is Quadrant 4. Coordinate for point B is seven comma one.