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 triangle

Isosceles right-angled triangle is a triangle whose two sides are equal

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

Clearly,

AB = BC

Thus, Δ ABC is an isosceles triangle

Hence Proved