Question

For what value of x are the points A(−3, 12), B(7, 6) and C(x, 9) collinear.

Answer 1

A(−3,12),B(7,6) and C(x,9) are the given points. Then:

(x₁ = −3, y₁ = 12), (x₂ = 7, y₂ = 6) and (x₃ = x, y₃ = 9)

It is given that points A, B and C are collinear. Therefore,

x₁(y_{2 −} y₃) + x₂(y_{3 −} y₁) + x₃(y_{1 −} y₂) = 0

⇒ (−3)(6 − 9) + 7(9 − 12) + x(12 − 6) = 0

⇒ (−3)(−3) + 7(−3) + x(6) = 0

⇒ 9 − 21 + 6x = 0

⇒ 6x − 12 = 0

⇒ 6x = 12

`⇒ x = 12/6 = 2`

Therefore, when  x = 2, the given points are collinear