Answer :

In a parallelogram, opposite sides are equal and parallel.

According to the distance formula, the distance 'd' between two points (a,b) and (c,d) is given by
.....(1)


For the given points, length PQ =


PQ =


Length QR =


QR = =


Length RS =


RS = =


Length SP =


SP = =


As PQ = RS and QR = SP


Checking for slopes


Slope of a line between two points (a,b) and (c,d) is



Slope PQ = = 1


Slope QR = =


Slope RS =


Slope SP =


As PQ = RS and their slope = 1


And


QR = SP and their slope = -1.


Hence the given points form a parallelogram.


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