Q. 73.6( 8 Votes )

# Show that the poi

Answer :

To prove: Points P, Q, R, S forms rectangle.

Formula:

The distance between two points (x_{1},y_{1},z_{1}) and (x_{2},y_{2},z_{2}) is given by

D=

Here,

(x_{1},y_{1},z_{1})= (2, 3, 5)

(x_{2},y_{2},z_{2})= (-4, 7, -7)

(x_{3},y_{3},z_{3})= (-2, 1, -10)

(x_{4},y_{4},z_{4})= (4, -3, 2)

Length PQ =

=

=

=

=

Length QR =

=

=

=

=

Length RS =

=

=

=

=

Length PS =

=

=

=

=

Length PR =

=

=

=

=

Length QS =

=

=

=

=

Here, PQ = RS which are opposite sides of polygon.

QR = PS which are opposite sides of polygon.

Also the diagonals PR = QS.

Hence, the polygon is a rectangle.

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