Question

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

(2, 7), (1, 1), (10, 8)

Answer 1

Area of ​​a triangle known from vertex units (x₁, y₁), (x₂, y₂), (x₃, y₃),

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

The area of triangle is given by,

Δ = `1/2 |(2,7,1),(1,1,1),(10,8,1)|`

= `1/2 [2|(1,1),(8,1)| - 7|(1,1),(10,1)| + 1|(1,1),(10,8)|]`

= `1/2 [2 (1 - 8) - 7 (1 - 10) + 1(8 - 10)]`

= `1/2 [-14 + 63 - 2]`

= `47/2`

= 23.5 sq. units