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.

Answer :

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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