If the points (a, 0), (o, b) and (1, 1) are collinear, prove that a + b = ab.

Question

Philoid · Accepted Answer

Given: – (a, 0), (o, b) and (1, 1) are collinear points

To Prove: – a + b = ab

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

⇒

⇒ a + b = ab

Hence Proved