Question

Prove that the points (2, – 2), (–3, 8) and (–1, 4) are collinear

Answer 1

Let ∆ be the area of the triangle formed by the given points.

We have,

`∴ ∆ = \frac { 1 }{ 2 } |{2 × 8 + (–3) × 4 + (–1) × (–2)} – {(–3) × (–2) + (–1) × 8 + 2 × 4}|`

`⇒ ∆ = \frac { 1 }{ 2 } |(16 – 12 + 2) – (6 – 8 + 8)|`

`⇒ ∆ = \frac { 1 }{ 2 } |6 – 6| = 0`

Hence, given points are collinear.