Show that the following points form an isosceles triangle.
(2, 3), (5, 7) and (1, 4)
Formula used: 
(2, 3), (5, 7) and (1, 4)
Let the point be A (5, 7) B (2, 3) and C (1, 4)
Distance of AB
⇒ AB = √ (2 – 5)2 + (3 – 7)2)
⇒ AB = √ ((–3)2 + (–4)2)
⇒ AB = √ (9 + 16)
⇒ AB = √ 25 = 5
Distance of AC
⇒ AC = √ ((1 – 5)2 + (4 – 7)2)
⇒ AC = √ ((–4)2 + (–3)2)
⇒ AC = √ (16 + 9)
⇒ AC = √ 25 = 5
Distance of BC
⇒ BC = √ ((1 – 2)2 + (4 – 3)2)
⇒ BC = √ ((–1)2 + (1)2)
⇒ BC = √ (1 + 1)
⇒ BC = √ 2
We notice that AB = AC = 5
∴ Points A, B and C are coordinates of an isosceles triangle.
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