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### Course: 8th grade foundations (Eureka Math/EngageNY) > Unit 7

Lesson 2: Topic C: Foundations- Perimeter & area
- Area of triangles
- Area of a parallelogram
- Area of trapezoids
- Area of composite shapes
- Area of composite shapes
- Surface area using nets
- Dimensions of a rectangle from coordinates
- Quadrilateral problems on the coordinate plane
- Quadrilateral problems on the coordinate plane

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# Dimensions of a rectangle from coordinates

How can we determine the length of a side of a rectangle given the coordinates of its vertices? In this example, by plotting the points on a graph, we can see that the length one side is five because the y-coordinate increases by five from one endpoint to the other.

## Want to join the conversation?

- But what if the vertices don't have the same x or y? How would you calculate the distance then?(17 votes)
- 1. if it is not, then it is not a rectangle anymore.

2.but if you really want to know, you could copy the picture and count, estimate,eg: a 1/4 to another 3/4 make one hole, a half and a half make one hole. normally the teacher will not give you these type of questions. it is hard to count.

3. You can also get more information on Khan too. here is the link https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-geometry-topic(18 votes)

- Couldn’t you just look at the coordinates of a and d, then look at the coordinate that is the same then look at the other ones then compare those, the answer would be the difference between the two(6 votes)
- Yes you could do that, and it was a faster solution.

But remember that the distance between the two points is an**absolute value**(can not be negative) of their difference.

In this example it is obvious that points (7,1) and (7,6) are the endpoints of the same side and the y-coordinate**increases by five**from one endpoint to the other. The difference between 6 and 1 is 5 (e.g., 6 - 1 = 5). Therefore the distance between the points is 5 units.

If the y-coordinates were negative such as (7,-1) and (7,-6) you could say that y-coordinate**decreases by five**. Which also means that the distance between the points is 5. But if you try to find the difference between -6 and -1 is will be -5 (e.g., -6 - (-1) = -5). Because distance must be positive the rule is to always look for the**absolute value**of the difference (e.g., |-5| = 5).

The cool thing about it is that you can find the distance by subtracting y-coordinates in any order. With the points (7,1) and (7,6) we can subtract 6 from 1, get -5, and the absolute value of that will be our distance! (e.g., Distance = |1 - 6| = |-5| = 5)(10 votes)

- how do you find the area(3 votes)
- To find the area of a rectangle you multiply the length times the width. Other shapes will have their own formulas for area.

An example of this would be if I had a rectangle that was 2 by 4 the area would be 8.(7 votes)

- why do y and x different meanings(1 vote)
- Because there are two different planes, so they have to be named differently.(4 votes)

- How did find the shape of the shape?(2 votes)
- you make points on the cordinates listed. do that until you see the shape and its closed.(3 votes)

- Hi hows ur guys's day 😁(2 votes)
- going well how about yours😁(3 votes)

- why did sal talk about the other points? doesnt he want to finish his job?(3 votes)
- How do you draw the whole coordinate grid i(1 vote)
- The grid is usually tricky and often hard to draw, so you can just create the cross, and with the numbers, perhaps count by fives to make a large amount with fewer numbers.(4 votes)

- hello bois me nfubrfdj(2 votes)
- hellllllllolok,kmjn bhv vfdsasertyhujn vcfgyhujikolp(2 votes)

## Video transcript

- [Instructor] Rectangle ABCD is graphed in the coordinate plane. The following are the
vertices of the rectangle, and they give us the labels
for the vertices as well. Given these coordinates, what is the length of
side AD of this rectangle? So let's just plot it. That's one way that we could tackle it. So let's, let me see all of these are actually in the first coordinate. So I can focus on the first coordinate. So let's say that's my y-axis. That's my y-axis. And let me draw my x-axis, my x-axis. And actually I wanna really focus in on the points A and D because we just need to find the length of the side
from point A to point D. So point A, lemme just use another color, so point A is at x equals 7, y is equal to 1. So 1, 2, 3, 4, 5, 6, 7, so that's x equals 7. y is equal to 1. y is equal to 1, so that is point A right over there, point A, let me label it, point A. And then where's point D? Point D has the exact same, has the exact same x-coordinate, but its y-coordinate
is a little bit higher. Its y-coordinate is 6, it's actually 5 higher. So point D is that x equals 7, y is equal to 6. So y is equal to 1, 2, 3, 4, 5, and 6. So that's y is equal to 6. And so we can draw the point. It is going to be right over here. This is point D, and we can actually connect
them with a line if we like to show that this is
a side of a rectangle. So let me draw that. I can just draw this like this. And there you have it. I haven't even drawn
the whole rectangle yet, but just by plotting these two points, we can think about how long side AD is. We can see, look, the x doesn't
change going from A to D, but we do increase in
the y direction by 5. We go from y is equal to 1 to y is equal to 6. So our change in y is equal to 5. So what's the length of this line? Well, it's gonna be 5. It's gonna be 5, whatever the units are. So that's the length of side AD. It's going to be equal to 5. We went from the point 7,1 to the point, to the point 7,6. Now they said that this was a rectangle, now just for satisfaction, we can draw the entire rectangle. We have the point B. That is at x equals 5, y is equal to 1. So let me draw that. And I'm just doing this just for fun now. At this point, we're
done with the problem. So x equals 5, y equals 1. That's right over here. That's point B. Let me write B, that's the point 5,1. And then we have the point C. I'll use another color. The point C is at x equals 5, y equals 6. x equals 5, y equals 6. Point C is right over here. Point C is the point x
equals 5, y equals 6. And then we can connect
all the dots if we like and clearly see that it is a rectangle. So I could connect those, I could connect these two, and then I could connect these two. And then we see that we
indeed have a rectangle. But we answered it a while ago that the length of side AD is equal to 5. If we cared about the other
sides, the length of BA, well, this is 2, a difference of 2 along the x direction, the horizontal direction, this difference of 2
along the x direction, difference of 5 in the y direction, we go from y equals 1 to y equals 6. So there you have it. We are actually able to figure out all of the dimensions of this rectangle.