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:

Hope this helps:)

Answer 2

`A=50\ units^2`

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=√(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=√(20)\ units`

The area of rectangle is equal to

`A=(√(125))(√(20))`

`A=50\ units^2`