Find a relation between x and y, if the points A(2, 1), B(x, y) 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{2(y–5) + x (5– 1) + 7 (1– y)}
⇒ 2y–10 + 4x–7–7y = 0
⇒ 4x –5y – 3 = 0