Question

What is the area of the rectangle?

40 units²
45 units²
50 units²
55 units²

A rectangle is graphed on a coordinate plane. The horizontal x-axis ranges from negative 10 to 10 in increments of 1. The vertical y-axis ranges from negative 10 to 10 in increments of 1. The vertices of the rectangle lie on begin ordered pair negative 5 comma 5 end ordered pair and begin ordered pair negative 1 comma 7 end ordered pair and begin ordered pair 4 comma negative 3 end ordered pair and begin ordered pair 0 comma negative 5 end ordered pair.

Answer 1

`50\ units^(2)`

Explanation:

Plot the figure to better understand the problem

see the attached figure

we know that

If the figure is a rectangle

then

`AB=CD \\AD=BC`

The area of the rectangle is equal to

`A=B*h`

where

B is the base

h is the height

the base B is equal to the distance AB

the height h is equal to the distance AD

Step 1

Find the distance AB

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

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

`A(-5,5)\\B(0,-5)`

substitute the values

`d=\sqrt{(-5-5)^(2)+(0+5)^(2)}\\d=\sqrt{(-10)^(2)+(5)^(2)}\\dAB=√(125)\ units`

Step 2

Find the distance AD

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

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

`A(-5,5)\\D(-1,7)`

substitute the values

`d=\sqrt{(7-5)^(2)+(-1+5)^(2)}\\d=\sqrt{(2)^(2)+(4)^(2)}\\dAD=√(20)\ units`

Step 3

Find the area of the rectangle

`A=AB*AD`

we have

`dAB=√(125)\ units\\dAD=√(20)\ units`

substitute

`A=√(125)*√(20)\\A=√(2,500)\\A=50\ units^(2)`