If the points (a, 1), (1, 2) and (0, b + 1) are collinear, then show that .

Let A (a, 1), B (1, 2) and C (0, b + 1) be the given points.

Slope of line passing through (x₁, y₁) and (x₂, y₂) is

Slope of AB

Slope of BC

If three points are collinear, then slope of AB is equal to slope of AC

∴ slope of AB = slope of BC

⇒ 1 = (–b + 1)(1 – a)

⇒ 1 = –b(1 – a) + 1(1 – a)

⇒ 1 = –b + ab + 1 – a

⇒ –b + ab – a = 0

⇒ ab – b = a

Dividing both sides by ab, we get

⇒

⇒

⇒

Hence proved.