Given: Points are A(3, 3, 3), B(0, 6, 3), C(1, 7, 7) and D(4, 4, 7)

To prove: the quadrilateral formed by these 4 points is a square

All sides of a square are equal

Formula used:

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

Therefore,

The distance between A(3, 3, 3) and B(0, 6, 3) is AB,

Distance between B(0, 6, 3) and C(1, 7, 7) is BC,

Distance between C(1, 7, 7) and D(4, 4, 7) is CD,

The distance between A(3, 3, 3) and D(4, 4, 7) is AD,

Clearly,

AB = BC = CD = AD

Thus, Quadrilateral formed by ABCD is a square

Hence Proved