Question

On a coordinate plane, rectangle W X Y Z is shown. Point W is at (negative 6, 6), point X is at (negative 4, 0), point Y is at (negative 7, negative 1), and point Z is at (negative 9, 5).
In the diagram, ZY = WX = 2 StartRoot 10 EndRoot. What is the perimeter of rectangle WXYZ?

StartRoot 10 EndRoot units
2 StartRoot 10 EndRoot units
6 StartRoot 10 EndRoot units
8 StartRoot 10 EndRoot units

Answer 1

Answer:

it is A. 6 StartRoot 10 EndRoot units

Answer 2

Answer:

6 StartRoot 10 EndRoot units

Step-by-step explanation:

step 1

Plot the coordinates of rectangle WXYZ to better understand the problem

we have

W(-6,6),X(-4,0),Y(-7,-1),Z(-9,5)

using a graphing tool

see the attached figure

step 2

Find out the perimeter

The perimeter of rectangle is equal to

$P=2(L+W)$

we have

$L=WX\\W=XY$

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

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

Find the distance WX

we have

W(-6,6),X(-4,0)

substitute in the formula

$d=\sqrt{(0-6)^{2}+(-4+6)^{2}}$

$d=\sqrt{(-6)^{2}+(2)^{2}}$

$d_W_X=\sqrt{40}\ units$

Find the distance XY

we have

X(-4,0),Y(-7,-1)

substitute in the formula

$d=\sqrt{(-1-0)^{2}+(-7+4)^{2}}$

$d=\sqrt{(-1)^{2}+(-3)^{2}}$

$d_X_Y=\sqrt{10}\ units$

step 3

Find the perimeter

$P=2(L+W)$

we have

$L=WX=\sqrt{40}\ units\\W=XY=\sqrt{10}\ units$

substitute

$P=2(\sqrt{40}+\sqrt{10})=2(2\sqrt{10}+\sqrt{10})=6\sqrt{10}\ units$