Question

Find the area of the triangle whose vertices are (–8, 4), (–6, 6) and (–3, 9).

Answer 1

Given that, the vertices of triangles are (–8, 4), (–6, 6) and (–3, 9).

Let (x₁, y₁) `→` (−8, 4)

(x₂, y₂) `→` (−6, 6)

And (x₃, y₃) `→` (−3, 9)

We know that, the area of triangle with vertices

(x₁, y₁), (x₂, y₂) and (x₃, y₃)

Δ = `1/2[x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)]`

= `1/2[-8(6 - 9) - 6(9 - 4) + (-3)(4 - 6)]`

= `1/2[-8(-3) - 6(5) - 3(-2)]`

= `1/2(24 - 30 + 6)`

= `1/2(30 - 30)`

= `1/2(0)`

= 0

Hence, the required area of triangle is 0.