Show that the points (0, 7, 10), (-1, 6, 6) and (-4, 9, 6) are the vertices of an isosceles 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 an isosceles right-angled triangle
Isosceles right-angled triangle is a triangle whose two sides are equal and also 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
Since, AB = BC
AB2 + BC2
= 18 + 18
= 36
= AC2
As, AB = BC and AB2 + BC2 = AC2
Thus, Δ ABC is an isosceles-right angled triangle
Hence Proved
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