Show that the following points form an isosceles triangle.
(1, 3), (−3, –5) and (−3, 0)
Formula used: 
(1, 3), (–3, –5) and (–3, 0)
Let the point be A (–3, 0) B (1, 3) and C (–3, –5)
Distance of AB
⇒ AB = √ ((1 – (–3))2 + (3 – 0)2)
⇒ AB = √ ((1 + 3)2 + (3 – 0)2)
⇒ AB = √ ((4)2 + (3)2)
⇒ AB = √ (16 + 9)
⇒ AB = √25 = 5
Distance of AC
⇒ AC = √ ((–3 – (–3))2 + (–5 – 0)2)
⇒ AC = √ ((–3 + 3)2 + (–5 + 0)2)
⇒ AC = √ ((0)2 + (–5)2)
⇒ AC = √ (0 + 25)
⇒ AC = √25 = 5
Distance of BC
⇒ BC = √ ((–3 – 1)2 + (–5 – 3)2)
⇒ BC = √ ((–4)2 + (–8)2)
⇒ BC = √ (16 + 64)
⇒ BC = √ 80
We notice that AB = AC = 5
∴ Points A, B and C are coordinates of an isosceles triangle.
3