Q19 of 157 Page 753

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

Find the value of y for which the points A(–3, 9), B(2, y) and C(4, –5) are collinear.

For what values of k are the points A(8, 1), B( 3, –2k) and C(k, –5) collinear.

Find a relation between x and y, if the points A(x, y), B(–5, 7) and C(–4, 5) are collinear.

Prove that the points A(a, 0), B(0, b) and C(1, 1) are collinear, if