Let the coordinate of $\mathrm{D}$ be $\left(\mathit{x},\mathit{y}\right)$. In a parallelogram, mid point of diagonal AC coincides with the mid-point of diagonal BD.

Mid point of $\mathrm{AC}=\left(\frac{3+3}{2},\frac{6+2}{2}\right)=\left(3,4\right)$
Mid point of $\mathrm{BD}=\left(\frac{\mathit{x}+5}{2},\frac{\mathit{y}+10}{2}\right)$
$\because$ Mid point of $\mathit{A}\mathit{C}=$ Mid point of $\mathit{B}\mathit{D}$
$\left(3,4\right)=\left(\frac{\mathit{x}+5}{2},\frac{\mathit{y}+10}{2}\right)$
Equating,


Coordinates of the fourth vertex $\mathrm{D}\left(1,-2\right)$