Show that the following points form an isosceles triangle.

(−2, 0), (4, 0) and (1, 3)

Formula used:

(–2, 0), (4,0) and (1, 3)

Let the point be A (1, 3) B (–2, 0) and C (4, 0)

Distance of AB

⇒ AB = √ ((–2 – 1)² + (0 – 3)²)

⇒ AB = √ ((–3)² + (–3)²)

⇒ AB = √ (9 + 9)

⇒ AB = √ 18 = 3√ 2

Distance of AC

⇒ AC = √ ((4 – 1)² + (0 – 3)²)

⇒ AC = √ ((3)² + (–3)²)

⇒ AC = √ (9 + 9)

⇒ AC = √ 18 = 3√2

Distance of BC

⇒ BC = √ ((4 – (–2))² + (0 – 0)²)

⇒ BC = √ ((6)² + (0)²)

⇒ BC = √ (36 + 0)

⇒ BC = √ 36 = 6

We notice that AB = AC =3√2

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