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If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

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Let A,B,C and D be the points (1,2) (4,y), (x,6) and (3,5) respectively.

Mid point of diagonal AC is image

and Mid point of Diagonal BD is image

Since the diagonals of a parallelogram bisect each other, the mid point of AC and BD are same.

∴ x+1/2 = 7/2 and 4 = 5+y/2

⇒ x + 1 = 7 and 5 + y = 8

⇒ x = 6 and y = 3

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