# 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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