Show that the following points form an equilateral triangle.

(0, 0), (10, 0) and (5, 5√3)

Formula used:

(0, 0), (10, 0) and (5, 5√3)

Let the points be A (0, 0), B (10, 0) and C (5, 5√3)

Distance of AB

⇒ AB = √ ((10 – 0)² + (0 – 0)²)

⇒ AB = √ ((10)² + (0)²)

⇒ AB = √ (100 + 0)

⇒ AB = √100

⇒ AB = 10

Distance of BC

⇒ B C= √ ((5 – 10)² + (5√3 – 0)²)

⇒ BC = √ ((–5)² + (5√3)²)

⇒ BC = √ (25 + 75)

⇒ BC = √100

⇒ BC = 10

Distance of AC

⇒ AC = √ ((5 – 0)² + (5√3 – 0))²)

⇒ AC = √ ((5)² + (5√3)²)

⇒ AC = √ (25 + 75)

⇒ AC = √ 100

⇒ AC = 10

∴ AB = BC = AC = 10

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