Question

What is the area of the rectangle?

Answer 1

Answer:

$A=50\ units^2$

Step-by-step explanation:

we know that

The area of rectangle is equal to

$A=LW$

The coordinates of vertices are

$A(-5,5),B(-1,7),C(4,-3),D(0,-5)$

using a graphing tool

Plot the coordinates of rectangle to better understand the problem

see the attached figure

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

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

we have that

$L=AD,W=AB$

Find out the distance AD

we have

$A(-5,5),D(0,-5)$

substitute in the formula

$L=\sqrt{(-5-5)^{2}+(0+5)^{2}}$

$L=\sqrt{(-10)^{2}+(5)^{2}}$

$L=\sqrt{125}\ units$

Find out the distance AB

we have

$A(-5,5),B(-1,7)$

substitute in the formula

$W=\sqrt{(7-5)^{2}+(-1+5)^{2}}$

$W=\sqrt{(2)^{2}+(4)^{2}}$

$W=\sqrt{20}\ units$

The area of rectangle is equal to

$A=(\sqrt{125})(\sqrt{20})$

$A=50\ units^2$