Q15 of 157 Page 753

For what value of x are the points A(–3, 12), B(7, 6) and C(x, 9) 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(6–9) + 7 (9 – 12) + x(12– 6)} = 0

⇒ (–3)(–3) + 7(–3) + 6x = 0

⇒ 9–21 + 6x = 0

6x = 12

x = 2

Show that the following points are collinear:

Find the value of x for which the points A(x, 2), B(–3, –4) and C(7, –5) are collinear.

For what value of y are the points P(1, 4), Q(3, y) and R(–3, 16) are collinear?

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