The vertices of a quad. PMQS are P (0, 0), M (3, 2), Q (7, 7) and S ( 4, 5). Show that PMQS is a parallelogram?Prove either of the following :(i) opposite sides are equal ;(ii) The mid-point of one diagonal in the same as that of the other diagonal.(iii) opposite sides are parallel.

We have, P0,0; M3,2;Q7,7;S4,5 as the given vertices of quadrilateral.Now, PQ and MS are the diagonals of quadrilateral PMQS.We know that coordinates of the mid point of the line segment joining the points x1,y1 and x2,y2 isx1+x22 and y1+y22Now, coordinates of mid point of PM  = 0+72,0+7272,72Coordinates of mid point of MS = 3+42,2+5272,72Since  coordinates of mid point of PM = Coordinates of mid point of MSDiagonals of quadrilateral PMQS bisect each otherPMQS is a parallelogram.

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