Q. 7

# Show that the points P(2, 3, 5), Q(-4, 7, -7), R(-2, 1, -10) and S(4, -3, 2) are the vertices of a rectangle.

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

Formula:

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

D=

Here,

(x1,y1,z1)= (2, 3, 5)

(x2,y2,z2)= (-4, 7, -7)

(x3,y3,z3)= (-2, 1, -10)

(x4,y4,z4)= (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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