Question

on a coordinate plane, the vertices of a rectangle are (2,4), (2,-1), (-5,-1) and (-5,4). What is the perimeter of the rectangle?

Answer 1

5+5+7+7 is equal to 24 which is the perimeter

Answer 2

`P=24\ units`

Explanation:

we know that

The perimeter of the rectangle is equal to

`P=2L+2W`

where

L is the length side

W is the width side

In this problem we have

`A(2,4),B(2,-1),C(-5,-1),D (-5,4)`

using a graphing tool

Plot the points

see the attached figure to better understand the problem

`L=BC`

`W=AB`

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

Find the distance BC

`B(2,-1),C(-5,-1)`

substitute

`dBC=\sqrt{(-1+1)^(2)+(-5-2)^(2)}`

`dBC=√(49)=7\ units`

Find the distance AB

`A(2,4),B(2,-1)`

substitute

`dAB=\sqrt{(-1-4)^(2)+(2-2)^(2)}`

`dAB=√(25)=5\ units`

Find the perimeter

we have

`L=dBC=7\ units`

`W=dAB=5\ units`

substitute

`P=2(7)+2(5)=24\ units`