Find the value of x for which the points A(x, 2), B(–3, –4) and C(7, –5) are collinear.
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)}
⇒ Δ = 1/2{x(–4 + 5)–3 (–5– 2) + 7 (2 + 4)} = 0
⇒ Δ = 1/2{x + 21 + 42} = 0
x = –63