Show that the following points form an equilateral triangle.

(√3, 2), (0,1) and (0, 3)

Formula used:

(√3, 2), (0, 1) and (0, 3)

Let the points be A (√3, 2), B (0, 1) and C (0, 3)

Distance of AB

⇒ AB = √ ((0 – √3)² + (1 – 2)²)

⇒ AB = √ ((√3)² + (–1)²)

⇒ AB = √ (3 + 1)

⇒ AB = √4

⇒ AB = 2

Distance of BC

⇒ B C= √ ((0 – 0)² + (3 – 1)²)

⇒ BC = √ ((0)² + (2)²)

⇒ BC = √ (0 + 4)

⇒ BC = √4

⇒ BC = 2

Distance of AC

⇒ AC = √ ((0 – √3)² + (3 – 2))²)

⇒ AC = √ ((√3)² + (1)²)

⇒ AC = √ (3 + 1)

⇒ AC = √ 4

⇒ AC = 2

∴ AB = BC = AC = 2

Since, all the sides are equal the points form an equilateral triangle.