Question

For what value of x will the points (x, – 1), (2, 1) and (4, 5) lie on a line?

Answer 1

Given points will be collinear if the area of the triangle formed by them is zero.

∴ Area of the triangle = 0

⇒ |{x × 1 + 2 × 5 + 4 × (-1)} - {(2 × (-1) + 4 × 1 + x × 5}| = 0

⇒ (x + 10 - 4) - (-2 + 4 + 5x) = 0

⇒ (x + 6) - (5x + 2) = 0

⇒ -4x + 4 = 0

⇒ x = 1

Hence, the given points lies on a line, if x = 1