Show that the following points form an isosceles triangle.

(−1, −3), (2, −1) and (−1, 1)

Formula used:

(−1, −3), (2, −1) and (−1, 1)

Let the point be A (2, –1) B (–1, –3) and C (–1, 1)

Distance of AB

⇒ AB = √ ((–1 – 2)² + (–3 – (–1))²)

⇒ AB = √ ((–1 – 2)² + (–3 + 1)²)

⇒ AB = √ ((–3)² + (–2)²)

⇒ AB = √ (9 + 4)

⇒ AB = √ 13

Distance of AC

⇒ AC = √ ((–1 – 2)² + (1 – (–1))²)

⇒ AC = √ ((–1 – 2)² + (1 + 1)²)

⇒ AC = √ ((–3)² + (2)²)

⇒ AC = √ (9 + 4)

⇒ AC = √ 13

Distance of BC

⇒ BC = √ ((–1 – (–1))² + (1 – (–3))²)

⇒ BC = √ ((–1 + 1))² + (1 + 3)²)

⇒ BC = √ ((0)² + (4)²)

⇒ BC = √ (0 + 16)

⇒ BC = √ 16

We notice that AB = AC = √13

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