Question

The value of a,which the points (a,2a),(3,1)and (-2,6)are collinear is

Answer 1

If the three points A (a, 2a), B (3, 1) and C (-2, 6) are collinear, then 
slopes of any two pairs of points will be equal.

Now, apply slope formula to find the slopes of the respective pairs of points:

Slope of AB = (1 – 2a)/ (3 – a)

Slope of BC = (6 – 1)/ (-2 – 3) and

Slope of AC = (6 – 2a) /(-2 – a)

Now, Slope of AB = Slope of BC

(1 – 2a)/ (3 – a) = 5/(-5)

(1 – 2a)/ (3 – a) = -1

a = 4/3.