Show that the following points are collinear:

A(8, 1), B(3, –4) and C(2, –5)

To show that the points are collinear, we show that the area of triangle is equilateral = 0

Δ = 0

Δ = 1/2{x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)}

⇒ 1/2{8(–4 + 5) + 3 (–5–1) + 2 (1 + 4)}

⇒ 1/2{8–18 + 10}

= 0

Hence collinear.