Question

Find the area of the triangle ABC A(-6,2) B(3,2) c(-2,6) D (-2,2)

Answer 1

Answer:

18 square units.

Step-by-step explanation:

Area of the triangle = ½*AB*CD

First of all, find the length of AB and CD using the distance formula, $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

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

A(-6, 2) => (x1, y1)

B(3, 2) => (x2, y2)

$AB = \sqrt{(3 -(-6))^2 + (2 - 2)^2}$

$AB = \sqrt{(9)^2 + (0)^2} = \sqrt{81} = 9$

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

C(-2, 6) => (x1, y1)

D(-2, 2) => (x2, y2)

$CD = \sqrt{(-2 -(-2))^2 + (2 - 6)^2}$

$CD = \sqrt{(0)^2 + (-4)^2} = \sqrt{16} = 4$

AB = 9

CD = 4

Area of rectangle = ½*AB*CD = ½*9*4 = 9*2 = 18 square units.