Find the value of k for which the points A(-2, 3), B(1, 2) and C(k, 0) are collinear.

Given: The points are A(-5, 1), B(1, 2) and C(k, 0)


To find: value of k


AB


= √37 units


BC


AC


Since the points are collinear, AB + BC = AC



Squaring both sides and rearranging,



On simplifying,





Squaring both sides,


64 – 96k + 36k2 = 37 × (k2 – 2k + 5)


64 – 96k + 36k2 = 37k2 – 74k + 185


Rearranging,


37k2 – 74k + 185 = 36k2 – 96k + 64


k2 + 22k + 121 = 0


(k + 11)2 = 0


k = -11


Therefore, the value of k for which the points A, B and C are collinear is –11.


1