Question

The value of k if the points a(2,3) b(4,k) and c(6,-3) are collinear is

Answer 1

Consider points A(2, 3) and B(4, k).

Slope = (k - 3)/(4 - 2) = (k - 3)/2.

Consider points A(2, 3) and C(6, -3).

Slope = (- 3 - 3)/(6 - 2) = -6/4 = -3/2.

If and only if three or more points are collinear, the slope between any two points will always be equal. So,

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

=> k - 3 = -3

=> k = - 3 + 3

=> k = 0

Hence 0 is the answer.