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

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 O of diagonal AC and BD also divides these diagonals.

Therefore, O is the mid-point of AC and BD.

By mid point formula, If (x, y) is the midpoint of the line joining points A(x1, y1) and B(x2, y2) Then,

If O is the mid-point of AC, then the coordinates of O are:

() = (, 4)

If O is the mid-point of BD, then the coordinates of O are:

(, ) = (, )

Since both the coordinates are of the same point O

Comparing the x coordinates we get,

x + 1 = 7

x = 6

And,

Comparing the y coordinates we get,

= 4

5 + y = 8

y = 3
Hence, x = 6 and y = 3.

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