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

(N/A) Let the vertices of the parallelogram $ABCD$ be $A(1, 2), B(4, y), C(x, 6),$ and $D(3, 5).$
In a parallelogram,the diagonals bisect each other at the same point $O.$
Therefore,$O$ is the midpoint of both diagonals $AC$ and $BD.$
The midpoint of diagonal $AC$ is given by $\left(\frac{1+x}{2}, \frac{2+6}{2}\right) = \left(\frac{x+1}{2}, 4\right).$
The midpoint of diagonal $BD$ is given by $\left(\frac{4+3}{2}, \frac{y+5}{2}\right) = \left(\frac{7}{2}, \frac{y+5}{2}\right).$
Since both represent the same point $O,$ we equate their coordinates:
$\frac{x+1}{2} = \frac{7}{2} \implies x+1 = 7 \implies x = 6.$
$4 = \frac{y+5}{2} \implies 8 = y+5 \implies y = 3.$
Thus,$x = 6$ and $y = 3.$