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

Lesson 15: Lesson 15: Shapes on a coordinate plane

# 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.
• 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.
• why do y and x different meanings
(1 vote)
• Because there are two different planes, so they have to be named differently.
• How did find the shape of the shape?
• you make points on the cordinates listed. do that until you see the shape and its closed.
• Hi hows ur guys's day 😁
• going well how about yours😁
• 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.