Answer
$P = \left( {4,6} \right)$
Work Step by Step
Let the coordinates of the point $P$ be $\left( {x,y} \right)$. Since the figure is a parallelogram, the following two vectors must be equivalent:
$\left( {7,8} \right) - \left( {x,y} \right) = \left( {7 - x,8 - y} \right)$ ${\ \ }$ and ${\ \ }$ $\left( {5,4} \right) - \left( {2,2} \right) = \left( {3,2} \right)$
Thus, $\left( {7 - x,8 - y} \right) = \left( {3,2} \right)$.
So, $P = \left( {4,6} \right)$.
