Answer :

P is the mid-point of AB

Coordinates of P = (-1, )

Similarly coordinates of Q, R and S are (2, 4), (5, ) and (2, -1) respectively

Length of PQ = [(-1 – 2)^{2} + ()^{2}]^{1/2}

=

Length of QR = [(2 – 5)^{2} + ()^{2}]^{1/2}

=

Length of RS = [(5 – 2)^{2} + (+ 1)^{2}]^{1/2}

=

Length of SP = [(2+ 1)^{2} + (-1 – )^{2}]^{1/2}

=

Length of PR = [(-1- 5)^{2} + (– )^{2}]^{1/2}

= 6

Length of QS = [(2 – 2)^{2} + (4 + 1)^{2}]^{1/2}

= 5

It can be observed that all sides of the given quadrilateral are of the same measure. However, the diagonals are ofdifferent lengths. Therefore, PQRS is a rhombus

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