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