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.