If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k - 1, 5k) are collinear

• Geometry (C10)

If the points A(k + 1, 2k), B(3k, 2k + 3) and C(5k - 1, 5k) are collinear, then find the value of k.

Solution

Points A, B and C are collinear.

Therefore,

½ [(k + 1)(2k + 3 – 5k) + 3k(5k – 2k) + (5k – 1)(2k – 2k – 3)] = 0

(k + 1)(3 – 3k) + 9k² – 3(5k – 1) = 0

2k² – 5k + 2 = 0

(k – 2)(2k – 1) = 0

k = 2, 1/2