Concept : 1 Mark
Application : 1 Mark
Calculation : 2 Marks
Consider a  parallelogram ABCD .
Let O be the point of intersection of the diagonals AC and BD

We know that diagonals of a parallelogram bisect each other.
$\Rightarrow$ O is the midpoint of both the digonals AC and BD
Now, coordinates of O as mid-point of BD are
$O(x,y)=\left(\frac{x_1+x_2}{2}\right),\left(\frac{y_1+y_2}{2}\right)$
$\Rightarrow O(a,b)=\frac{4+3}{2},\frac{y+5}{2}\dots \dots \left(1\right)$ 
Also, coordinates of O as mid-point of AC are
$O(a,b)=\frac{1+x}{2},\frac{2+6}{2}\dots \dots \left(2\right)$
From (1) and (2), we have
$\frac{4+3}{2}=\frac{1+x}{2}$
$\frac{7}{2}=\frac{1+x}{2}\Rightarrow x=6$
And $\frac{y+5}{2}=\frac{2+6}{2}$
$\frac{y+5}{2}=\frac{8}{2}\Rightarrow y=3$