Question

What is the area of the rectangle shown on the coordinate plane?

Answer 1

The area of the rectangle would be 21 units.

Answer 2

Answer:

The area of rectangle is 42 square unit.

Step-by-step explanation:

We are given a rectangle shown in diagram.

We need to find the area of rectangle.

$\text{Area of rectangle }=L\times B$

First we have to find the L and B of the rectangle.

Using coordinate system find the coordinate of vertex of rectangle.

Using distance formula to find the distance of leg of rectangle.

A(2,-1)     B(9,-8)     C(12,-5)  

Distance formula:

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

$L=AB=\sqrt{(2-9)^2+(-1+8)^2}=7\sqrt2$

$B=BC=\sqrt{(12-9)^2+(-5+8)^2}=3\sqrt2$

$\text{Area of rectangle }=7\sqrt2\times 3\sqrt2 = 42\text{ Square Unit}$

Hence, The area of rectangle is 42 square unit.