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Question

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

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Solution



Let (1,2), (4,y), (x,6) and (3,5) are the coordinates of A,B,C,D vertices of a parallelogram ABCD, intersection point of diagonal AC and BD also divides these diagonals.
Therefore, O is the mid-point of AC and BD.
If O is the mid-point of AC, then the coordinates of O are
(1+x2,2+62)(frac1+x2,4)
If O is the mid-point of BD, then the coordinates of O are
(4+32,5+y2)(72,5+y2)
Since bothe the coordinates are of the same point O,
frac1+x2=frac72and4=frac5+y2
x+1=7 and 5+y=8
x=6andy=3

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