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

Question

Philoid · Accepted Answer

To show that the points are collinear, we show that the area of triangle is equilateral = 0

Δ = 0

Δ = 1/2{x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)} = 0

⇒ Δ = 1/2{a(b– 1) + 0 (1– 0) + 1 (0– b)} = 0

⇒ (ab–a–b) = 0

Dividing the equation by ab.

1–1/b–1/a

1–(1/a + 1/b)

1–1 = 0

Hence collinear.