Question

By using determinant, show that the following points are collinear: P(5, 0), Q(10, –3), R(–5, 6)

Answer 1

Here, P(x₁, y₁) ≡ P(5, 0), Q(x₂, y₂) ≡ Q(10, –3), R(x₃, y₃) ≡ R(–5, 6)
If A(ΔPQR) = 0, then the points P, Q, R are collinear.

∴ A(ΔPQR) = `1/2|(5, 0, 1),(10, -3, 1),(-5, 6, 1)|`

= `1/2[5(-3 - 6) - 0(10 + 5) + 1(60 - 15)]`

= `1/2(-45 + 0 + 45)` = 0

∴ A(ΔPQR) = 0
∴ Points P, Q and R are collinear.