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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?
• 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.
• Why do the teachers do only the easy stuff and never explain the hard stuff we end up doing? that isnt really good teaching
• That's probably because they want to do the easy stuff and make you do the hard stuff.
• I dont get why some people in the comment section think its cool to post random things but questions, and also how do I find the area again if someone would like to help me thank you very much!<3
• The formula for area is base*height. For example, if I had a rectangle, if the base was 4 and the height was 2. I would multiply them and the area would be 8. Hope this helped!
• 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
• 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)
• how do you find the area
• 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.
• Mrs. butindaro's class is the best.
• Hi hows ur guys's day 😁
• going well how about yours😁
• why do y and x different meanings
• Because there are two different planes, so they have to be named differently.
• how do you find the area
• You can find the area by multiplying the height and the width of a rectangle or square.

So if my rectangle is 6 units tall and 4 units wide, we can find the area by solving `6 x 4`. The result of that sum is 24, so I can safely say that the area of my rectangle is 24 units!

I hope this helps, Oliver1! :)
• How do you draw the whole coordinate grid i
• 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.

## Video transcript

- [Voiceover] 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 could focus on the first coordinate. So let's say that's my y-axis. It'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, let me do this in another color. So point A is at x equals seven, y is equal to one. So one, two, three, four, five, six, seven, so that's x equals seven. Y is equal to one. Y is equal to one, 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 x-coordinate, but its y-coordinate is a little bit higher. Its y-coordinate is six. It's actually five higher. So point D is at x equals seven, y is equal to six. So y is equal to one, two, three, four, five, and six. So that's y is equal to six, and so we can draw the point. It is going to be right over here. This is point D, and we could actually connect them with a line, if we like, to show that this is a side of a rectangle. 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 could say, look, the x doesn't change going from A to D, but we do increase in the y direction by five. We go from y is equal to one to y is equal to five, to y is equal to six. So our change in y is equal to five. So what's the length of this line? Well, it's gonna be five. It's gonna be five, whatever the units are. So that's the length of side AD. It's going to be equal to five. We went from the point (7, 1) to the point (7, 6). Now, they said that this was a rectangle. Now, just for our satisfaction, we can draw the entire rectangle. We have that point B that is at x equals five, y is equal to one, 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 five, y equals one. 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 do this in another color. The point C is at x equals five, y equals six. X equals five, y equals six. Point C is right over here. Point C is the point x equals five, y is equal to six. And then we could 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. Then I could connect these two. And then we see that we indeed have a rectangle. But we answered it awhile ago that the length of side AD is equal to five. If we cared about the other sides, the length of BA, well, this is two. a difference of two along the x direction, the horizontal direction, difference of two along the x direction, difference of five in the y direction. We go from y equals one to y equals six. So there you have it. We actually will figure out all of the dimensions of this rectangle.