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.

 Intersectionpoint O 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:

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

Since both the coordinates are of the same point O

x + 1 = 7

x = 6

And,

5 + y = 8

y = 3