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

1) 20 square units
2) 30 square units
3) 35 square units
4) 45 square units

Answer 1

Option 2) 30 square units

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=√(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=√(45)\ units`

step 3

Find the area of rectangle

The area of rectangle is equal to

`A=LW`

we have

`L=BC=√(45)\ units`

`W=AB=√(20)\ units`

substitute

`A=(√(45))(√(20))=√(900)=30\ units^2`