Q. 84.4( 81 Votes )

ABCD is a rectang

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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