Q. 175.0( 6 Votes )

There are four points P(2, –1), Q(3, 4), R(–2, 3) and S(–3, –2) in a plane. Then prove that PQRS in not a square, rather it is a rhombus.

Answer :

We have P (2,–1)


Q (3,4)


R (–2,3)


S (–3,–2)


Using the distance formula,


PQ =


=


=


=


QR =


=


=


=


RS =


=


=


=


SP =


=


=


=


All four sides of quadrilateral PQRS are equal.


Consider the diagonals, AC and BD.


PR =


=


=


=


QS =


=


=


=


Since the diagonals are not equal, the given quadrilateral is not a square.


PQRS is a rhombus.


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