Question

Mr. Janas is building a pool in his backyard. He sketches the rectangular pool on a coordinate plane. The vertices of the pool are A(-5,7),B( 1,7),C(1,-1),and D(-5,-1). If each unit represents 1 yard,how much area of the backyard is needed for the pool?

Answer 1

Answer: The area of the pool is 48 yard square.

Explanation:

It is given that the vertices of the pool are A(-5,7),B( 1,7),C(1,-1),and D(-5,-1).

Plot these points on a coordinate plane as shown below.

From the figure it is noticed that the length of the pool is AB, which is equal to 6 and the bright of the pool is BC, which is equal to 8.

It is also calculated by distance formula.

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The length AB is,

$AB=\sqrt{(1+5)^2+(7-7)^2} =6$

The breadth BC is,

$BC=\sqrt{(1-1)^2+(-1-7)^2} =8$

The area of a rectangle is the product of length and breadth of the rectangle.

$A=l\times b$

$A=6\times 8=48$

Since one unit represents one yard, therefore the area of the rectangular po is 48 yard square.