Show that the following points are collinear.

(1, 4), (3, −2) and (−1, 10)

Formula used:

(1, 4), (3, –2) and (–1, 10)

Let A (–1, 10), B (1, 4) and C (3, –2)

Distance of AB

⇒ AB =√ ((1 – (–1))² + (4 – 10)²)

⇒ AB = √ ((1 + 1)² + (4 – 10)²)

⇒ AB = √ (2)² + (–6)²

⇒ AB = √ (4 + 36)

⇒ AB = √ 40

Distance of BC

⇒ BC =√ ((3 – 1)² + (–2 – 4)²)

⇒ BC = √ (2)² + (–6)²

⇒ BC = √ (4 + 36)

⇒ BC = √ 40

Distance of AC

⇒ AC =√ ((3 – (–1))² + (–2 – 10)²)

⇒ AC = √ ((3 + 1)² + (2 – 10)²)

⇒ AC = √ (4)² + (–8)²

⇒ AC = √ (16 + 64)

⇒ AC = √ 80

i.e. AB + BC = AC

⇒ √40 + √40 = √80

∴ A, B and C are collinear.