Verify the following:

(0, 7, 10), (-1, 6, 6) and (2, -3, 4) are vertices of a right-angled triangle

Given: Points are A(0, 7, 10), B(-1, 6, 6) and C(-4, 9, 6)


To prove: the triangle formed by given points is a right-angled triangle


Right-angled triangle satisfies Pythagoras Theorem


Formula used:


The distance between any two points (a, b, c) and (m, n, o) is given by,



Therefore,


Distance between A(0, 7, 10) and B(-1, 6, 6) is AB,







Distance between B(-1, 6, 6) and C(-4, 9, 6) is BC,







Distance between A(0, 7, 10) and C(-4, 9, 6) is AC,






= 6


AB2 + BC2



= 18 + 18


= 36


= AC2


As, AB2 + BC2 = AC2


Thus, Δ ABC is a right angled triangle


Hence Proved


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