Question

If the points (-3,6), (-9,a) and (0,15) are collinear, then find a.

Answer 1

Let the given points be A(-3,6), B(-9,a) and C(0,15).

Slope of AB = $\frac{a-6}{-9+3}=\frac{6-a}{6}$

Slope of BC = $\frac{a-15}{-9-0}=\frac{15-a}{9}$

Since the points A, B and C are collinear.

Slope of AB = Slope of BC

$\frac{6-a}{6}=\frac{15-a}{9}$

$18-3a=30-2a$

$a=-12$