The triangle obtained by joining the points A (–5, 0) B (5, 0) and C (0, 6) is

Formula used:

Let the point be A (–5, 0) B (5, 0) and C (0, 6)

Distance of AB

⇒ AB = √ (5 – (–5))² + (0 – 0)²)

⇒ AB = √ (5 + 5)² + (0 – 0)²)

⇒ AB = √ ((10)² + (0)²)

⇒ AB = √ (100 + 0)

⇒ AB = √ 100 = 10

Distance of AC

⇒ AC = √ ((0 – (–5))² + (6 – 0)²)

⇒ AC = √ ((5)² + (6)²)

⇒ AC = √ (25 + 36)

⇒ AC = √ 61

Distance of BC

⇒ BC = √ ((0 – 5)² + (6 – 0)²)

⇒ BC = √ ((–5)² + (6)²)

⇒ BC = √ (25 + 36)

⇒ BC = √ 61

We notice that BC = AC = √ 61

∴ Points A, B and C are coordinates of an isosceles triangle.