Question

Show that the points (a, 0), (0, b) and (3a, – 2b) are collinear.

Answer 1

Let the given points be

P(x₁, y₁) = (a, 0), Q(x₂, y₂) = (0, b) and

R(x₃, y₃) = (3a – 2b).

∴ Area of ∆PQR = \(\frac{1}{2}\)|x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)|

= \(\frac{1}{2}\)|a(b + 2b) + 0(−2b − 0) + 3a(0 − b)|

= 0

⇒ the points (a, 0), (0, b) and (3a, – 2b) are collinear.