If the points A$\displaystyle (4, 5)$, B(m, $\displaystyle 6$), C$\displaystyle (4, 3)$ and D($\displaystyle 1$, n) taken in this order are the vertices of a parallelogram ABCD, then find the values of m and n.

Coordinates of mid-point of AC = Coordinates of mid-point of BD \(\displaystyle \left(\frac{4+4}{2}, \frac{5+3}{2}\right)=\left(\frac{1+\mathrm{m}}{2}, \frac{\mathrm{n}+6}{2}\right)\) \(\displaystyle \mathrm{m}=7\) \(\displaystyle \mathrm{n}=2\)