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.

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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Chemical Co-ordination VS Neural Co-ordination48 mins
Some Interesting Proofs in Geometry36 mins
Quiz | Chemical Co-ordination47 mins
Quiz | Neural Co-ordinataion51 mins
Section Formula30 mins
Previous Year RMO Questions43 mins
NCERT | Most Important Proofs for Boards28 mins
Foundation | Human Endocrine System58 mins
Human Brain52 mins
Tropic and Nastic Movements32 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses