Question

Triangle GHI, with vertices G(-8,-8), H(-6,-7), and I(-9,-2),

What is the area, in square units, of triangle GHI

Answer 1

area = 6.5 square units

Explanation:

Use the area of a triangle in coordinate geometry formula:

`\triangle GHI =(1)/(2) |x_1(y_2- y_3) + x_2(y_3 -y_1) + x_3(y_1 -y_2)|`

where
`(x_1,y_1)=(-8,-8) \ \ \ \ (x_2,y_2)=(-6,-7) \ \ \ \ (x_3,y_3)=(-9,-2)`

`\triangle GHI =(1)/(2) |x_1(y_2- y_3) + x_2(y_3 -y_1) + x_3(y_1 -y_2)|`

`\implies \triangle GHI =(1)/(2) |-8(-7+2) -6(-2 +8) -9(-8 +7)|`

`\implies \triangle GHI =(1)/(2) |40 -36 +9|`

`\implies \triangle GHI =6.5`