Q20 of 157 Page 753

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

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(2, 1), B(x, y) and C(7, 5) are collinear.

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

If the points P(–3, 9), Q(a, b) and R(4, –5) are collinear and a + b = 1, find the values of a and b.