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Question

Prove that the points (0,7,10),(1,6,6) and (4,9,6) are the vertices of an isosceles triangle.

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Solution

Let A=(0,7,10), B=(1,6,6) AND C=(4,9,6) then:
AB=(1)2+(1)2+(4)2=18
BC=(3)2+(3)2+(0)2=18
CA=(4)2+(2)2+(4)2=6

Since these lengths satisfy the triangle inequality and AB=BC, it is clear that these points form an isosceles triangle.


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