Question

The vertices of a rectangle are located at (1, 2) (5, 0) (2, -6) and (-2, -4) what is the area of the rectangle

Answer 1

Answer:

Option 2) 30 square units

Step-by-step explanation:

step 1

Plot the rectangle to better understand the problem

we have

A(1, 2),B(5, 0),C(2, -6) and D(-2, -4)

see that attached figure

step 2

Find the length of the sides

Remember that'

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

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

Find the length side AB

we have

A(1, 2),B(5, 0)

substitute in the formula

$d=\sqrt{(0-2)^{2}+(5-1)^{2}}$

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

$d_A_B=\sqrt{20}\ units$

Find the length side BC

we have

B(5, 0),C(2, -6)

substitute in the formula

$d=\sqrt{(-6-0)^{2}+(2-5)^{2}}$

$d=\sqrt{(-6)^{2}+(-3)^{2}}$

$d_B_C=\sqrt{45}\ units$

step 3

Find the area of rectangle

The area of rectangle is equal to

$A=LW$

we have

$L=BC=\sqrt{45}\ units$

$W=AB=\sqrt{20}\ units$

substitute

$A=(\sqrt{45})(\sqrt{20})=\sqrt{900}=30\ units^2$