Show that the following points are collinear:

A(–5, 1), B(5, 5) and C(10, 7)

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


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


⇒ Δ = 1/2{–5(5– 7) + 5 (7–1) + 10 (1–5) }


⇒ Δ = 1/2{10 + 30–40}


⇒ Δ = 0


Hence collinear.


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