Show that the points A(3, 3, 3), B(0, 6, 3), C(1, 7, 7) and D(4, 4, 7) are the vertices of squares.
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