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

Answer:

$P=24\ units$

Step-by-step 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

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

$dBC=\sqrt{49}=7\ units$    

Find the distance AB

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

substitute

$dAB=\sqrt{(-1-4)^{2}+(2-2)^{2}}$    

$dAB=\sqrt{25}=5\ units$    

Find the perimeter

we have

$L=dBC=7\ units$  

$W=dAB=5\ units$    

substitute

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