Question

Find the area of a triangle with vertices at the point given in the following:

(−2, −3), (3, 2), (−1, −8)

Answer 1

Area of ​​the triangle passing through the vertices (x₁, y₁), (x₂, y₂), (x₃, y₃),

Δ = `1/2 |(x_1,y_1,1),(x_2,y_2,1),(x_3,y_3,1)|`

Δ = `1/2 |(-2,-3,1),(3,2,1),(-1,-8,1)|`

= `1/2 [-2|(2,1),(-8,1)| + 3|(3,1),(-1,1)| + 1|(3,2),(-1,-8)|]`

= `1/2 [-2 ( 2 + 8) + 3 (3 + 1) + 1(-24 + 2)]`

= `1/2 [-2 (10) + 3 (4) + 1(- 22)]`

= `1/2 [-20 + 12 - 22]`

= `-30/2`

= −15

∴ Area = 15 square units (As area > 0)