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in 3D Coordinate Geometry by (32.9k points)
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Are the points A(3, 6, 9), B(10, 20, 30) and C(25, -41, 5), the vertices of a right-angled triangle?

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Given: Points are A(3, 6, 9), B(10, 20, 30) and C(25, -41, 5) 

To check: the triangle formed by given points is a right-angled triangle or not A right-angled triangle is a triangle which satisfies Pythagoras Theorem 

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

  \(\sqrt{(a−m)^2+(b−n)^2+(c−0)^2}\)

Therefore, 

The distance between A(3, 6, 9) and B(10, 20, 30) is AB,

Distance between A(3, 6, 9) and C(25, -41, 5) is AC,

Thus, Δ ABC is not a right angled triangle

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