Question

Prove that the points A(a,0), B(0,b) and C(1,1) are collinear, if (1/a + 1/b) = 1.

Answer 1

Consider the points A(a,0), B(0,b) and C(1,1).

Here, (x₁ = a,y₁ = 0).(x₂ = 0,y₂ = b) and (x₃ = 1,y₃ = 1).

It is given that the points are collinear. So,

Dividing the equation by ab:

Therefore, the given points are collinear if \((\frac{1}{a}+\frac{1}{b})=1.\)