Question

What is the perimeter of a rectangle with vertices at (4,4), (5, 1), (-1,-1) and (-2, 2)?

Answer 1

First, draw the figure with the coordinate points.

Now, find the distance between points: (-2,2) and (4,4)

`D=\sqrt[]{(x2-x1)^2+(y2-y1)^2}`
`D=\sqrt[]{(4-(-2))^2+(4-2)^2}=\sqrt[]{6^2+2^2}=\sqrt[]{40}=6.32`

We have the length of the rectangle.

To find the width, calculate the distance between points (-2,2) and (-1,-1)

`D=\sqrt[]{(-1-(-2))^2+(-1-2)^2}=\sqrt[]{(-1+2)^2+(-3)^2}=\sqrt[]{1+9}=\sqrt[]{10}=3.16`

Finally, we have:

Length: 6.32

Width: 3.16

Perimeter of a rectangle:

P = 2w+2L

P = 2 (6.32)+ 2 (3.16) = 18.97 = 19