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Question

In the graph, P and Q are two vertices of quadrilateral PQRS.
Given that coordinates of R and S are (4,2) and (1,1) respectively, the quadrilateral
PQRS is a

106110_e00d759df1b2419180232a0fed404c6c.png

A
rectangle
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B
square
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C
rhombus
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D
trapezium
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Solution

The correct option is B square
P(2,2);Q(1,5);R(4,2);S(1,1)
PQ=(1+2)2+(52)2=32QR=(41)2+(52)2=32RS=(41)2+(12)2=32PS=(1+2)2+(2+1)2=32PR=(4+2)2+(22)2=6QS=(11)2+(5(1))2=6
Since, all sides PQ,QR,RS and PS are equal,
also, diagonals PR and QS are also equal to each other,
We can say say that PQRS is a square.

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