Question

If points A(–3, 12), B(7, 6) and C(x, 9) are collinear, then the value of x is ______.

Answer 1

If points A(–3, 12), B(7, 6) and C(x, 9) are collinear, then the value of x is 2.

Explanation:

The points are collinear, then area of triangle = 0

∴ `1/2 [x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)] = 0`

⇒ `1/2 [-3(6 - 9) + 7(9 - 12) + x(12 - 6)] = 0`

⇒ `1/2 (9 - 21 + 6x) = 0`

⇒ `1/2 (-12 + 6x) = 0`

⇒ 6x = 12

⇒ x = 2