Q16 of 157 Page 753

For what value of y are the points P(1, 4), Q(3, y) and R(–3, 16) 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{1(y–16) + 3 (16–4)–3 (4–y)} = 0

⇒ y–16 + 36–12 + 3y = 0

⇒ 8 + 4y = 0

⇒ 4y = –8

y = –2

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 x are the points A(–3, 12), B(7, 6) and C(x, 9) collinear?

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.