Answer :

Three points are collinear if the area of triangle formed by them is zero.

Area of a triangle


0 = (k + 1)(2k + 3 – 5k) + 3k(5k – 2k) + (5k – 1)(2k – 2k – 3)


0 = (k + 1)(3 – 3k) + 3k(3k) + (5k – 1)(-3)


0 = -3k2+ 3 + 9k2 – 15k + 3


6k2 – 15k + 6 = 0


6k2 – 12k – 3k + 6 = 0


6k(k – 2) – 3(k – 2) = 0


(6k – 3)(k – 2) = 0


k = 2 or k = 1/2


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