Find a relation between x and y, if the points A(x, y), B(–5, 7) 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{x (7–5) + (–5) (–5–y) –4 (y– 7)}
⇒ 7x–5x–25 + 5y–4y + 28 = 0
⇒ 2x + y + 3 = 0