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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