Show that the following points are collinear:
A(2, – 2), B(–3, 8) and C(–1, 4)
To show that the points are collinear, we show that the area of triangle is equilateral = 0
Given, the area of the triangle, Δ = 0
⇒ Δ = 1/2(x1(y2−y3) + x2(y3−y1) + x3(y1−y2))
⇒ Δ = 1/2{2 (8– 4) + (–3) (4 + 2) –1 (2– 8)}
⇒ Δ = 1/2 {8–18 + 10}
⇒ Δ = 0
Hence the points A(2, – 2), B(–3, 8) and C(–1, 4) are collinear.