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

Quadratic Equations (10)

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

Answer

Points A, B and C are collinear. Therefore,

$\frac{1}{2}$ [(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, $\frac{1}{2}$

• Exam Year: 2017