If the points A(2, 3), B(5, k) and C(6, 7) are collinear then

Three points A, B, C are said to be collinear if,

Area of triangle formed by three points is zero

The formula of Area of Triangle of three points is given as follows:

Area, A = 0

⇒ = 0

⇒ 1/2 × {[-3k + 21] – [-3 + k]} = 0

⇒ -4k + 21 + 3 = 0

⇒ 4k = 24

⇒ k = 6

Therefore the value of k is 6.