Question

HELP! What is the area of the rectangle shown on the coordinate plane? Enter your answer in the box. Do not round at any steps.

___ units²

Answer 1

Answer:
`42 units^2`

Explanation:

Answer 2

`A=42\ units^(2)`

Explanation:

see the attached figure with letters to better understand the problem

we know that

The figure ABCD is a rectangle

so

`AB=CD \\AD=BC`

The area of a 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 BC

Let

`A(2,-1),B(9,-8),C(12,-5),D(5,2)`

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(2,-1),B(9,-8)`

substitute the values

`d=\sqrt{(-8+1)^(2)+(9-2)^(2)}`

`d=\sqrt{(-7)^(2)+(7)^(2)}`

`dAB=√(98)=7√(2)\ units`

Step 2

Find the distance BC

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

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

`B(9,-8),C(12,-5)`

substitute the values

`d=\sqrt{(-5+8)^(2)+(12-9)^(2)}`

`d=\sqrt{(3)^(2)+(3)^(2)}`

`dBC=√(18)=3√(2)\ units`

Step 3

Find the area

`A=B*h`

we have

`B=7√(2)\ units`

`h=3√(2)\ units`

substitute

`A=7√(2)*3√(2)=42\ units^(2)`