Find the value of y for which the points A(–3, 9), B(2, y) and C(4, –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{–3(y + 5) + 2 (–5–9) + 4 (9–y)} = 0
⇒ –3y–15–28 + 36–4y = 0
⇒ 7y = 36–43
y = –1