# Show that the poi

To prove: Points A, B, C, D form square.

Formula:

The distance between two points (x1,y1,z1) and (x2,y2,z2) is given by

D=

Here,

(x1,y1,z1)= (1, 1, 1)

(x2,y2,z2)= (-2, 4, 1)

(x3,y3,z3)= (-1, 5, 5)

(x4,y4,z4)= (2, 2, 5)

Length AB =

=

=

=

=

Length BC =

=

=

=

=

Length CD =

=

=

=

=

=

=

=

=

Length AC =

=

=

=

=

Length BD =

=

=

=

=

Here, AB = BC = CD = AD

Also, AC = BD

This means all the sides are the same and diagonals are also equal.

Hence vertices A, B, C, D form a square.

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