Show that points P(2, -2), Q(7, 3), R(11, -1) and S (6, -6) are vertices of a parallelogram.

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.