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Question

Determine whether the points are vertices of a right triangle A(3,4), B(2,6) and C(6,10)

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Solution

Using the distance formula d=(x2x1)2+(y2y1)2, we get
AB2=(2+3)2+(6+4)2=52+102=25+100=125
BC2=(6,2)2+(106)2=(8)2+42=64+16=80
CA2=(6+3)2+(10+4)2=(3)2+(14)2=9+196=205
i.e., AB2+BC2=125+80=205=CA2
Hence ABC is a right angled triangle since the square of one side is equal to sum of the squares of the other two sides.

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