Show that the following points are collinear.

(3, −2), (−2, 8) and (0, 4)

Formula used:

(3, 2), (–2, 8) and (0, 4)

Let A (–2, 8), B (0, 4) and C (3, 2)

Distance of AB

⇒ AB = √ ((0 – (–2))² + (4 – 8)²)

⇒ AB = √ (2)² + (–4)²

⇒ AB = √ (4 + 16)

⇒ AB = √20

Distance of BC

⇒ BC = √ ((3 – 0)² + (2 – 4)²)

⇒ BC = √ (3)² + (–2)²

⇒ BC = √ (9 + 4)

⇒ BC = √13

Distance of AC

⇒ AC = √ ((3 – (–2))² + (2 – 8)²)

⇒ AC = √ (5)² + (–6)²

⇒ AC = √ (25 + 36)

⇒ AC = √ 61