Given: – (a, b) (a’, b’) and (a – a’, b – b’) are points and ab’ = a’b

To Prove: – (a, b) (a’, b’) and (a – a’, b – b’) are collinear points

Proof: –

Tip: – If three points to be collinear, then the area of the triangle formed by these points will be zero.

Now, we know that,

vertices of a triangle are (x₁,y₁), (x₂,y₂) and (x₃,y₃), then the area of the triangle is given by:

Thus

Expanding along R₁

⇒

⇒

⇒

⇒ ab^’ – a^’b = 0

⇒ ab^’ = a^’b

Hence, Proved.