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.