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.