Q. 53.8( 39 Votes )

# Show that points

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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