Question

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

Enter your answer in the box. Do not round at any steps.

Answer 1

12

Explanation:

A (-4,1) B(-1,-2) C(-3,-4) D(-6,-1)

AB² = (-1 - (-4))² + (-2 -1)² = 18

AB = 3√2

BC² = (-3 - (-1))² + (-4 - (-2))² = 8

BC = 2√2

Area: AB x BC = 3√2 x 2√2 = 12

Answer 2

Area of the rectangle = 12 sq.units

Explanation:

To find the area of the rectangle shown in the figure,we have to find the length and breadth of it which inturn can be found by applying distance formula between two points.

Step 1:

Identifying the points from the graph

The 4 corners of the rectangle are:

(-4,1) , (-1,-2) , (-3,-4) , (-6,-1)

Step 2:

Applying distance formula to find length and breadth.

Distance formula =
`\sqrt{(x_2-x_1)^(2)+(y_2-y_1)^(2)}`

Length =
`\sqrt{(-1+4)^(2)+(-2-1)^(2)}=3√(2)\ units`

Breadth =
`\sqrt{(-1+3)^(2)+(-2+4)^(2)}=2√(2)`

Step 3:

Area = length×breadth

=
`3√(2)*2√(2)=12\ square\ units`