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Question

The points P(4,3),Q(6,4),R(5,6) and S(3,5) respectively are the vertices of a quadrilateral which is

A
a Square
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B
a Trapezium
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C
a Parallelogram
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D
a Rhombus
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Solution

The correct option is A a Square
PQ=(46)2+(34)2=5 units
QR=(65)2+(46)2=5 units
RS=(53)2+(65)2=5 units
PS=(43)2+(35)2=5 units

PR=(45)2+(36)2=10 unitsQS=(63)2+(45)2=10 units
So,
PQ=QR=RS=SP
And
PR=QS

Hence, it is a square.

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