Question

Find the value of k, if the points A (7, -2), B (5, 1) and C (3, 2k) are collinear.

Answer 1

The value of k is equal to 1.

For the points A (7, -2), B (5, 1) and C (3, 2k) to be collinear , slopes of any two pairs of points out of three points should be same.

Slope of AB = (1+2)/(5-7) = -3/2

Slope of AC = (2k+2)/(3-7) = -(k+2)/2

The Slope of AB and AC should be same , as the points are collinear.

Slope of AC = Slope of AB

=> -(k+2)/2 = -3/2

=> k+2 = 3

=> k = 1

We get the value of k equal to 1.