Problem

In the parallelogram $ABCD$, the coordinates of $A$ are $(3,7)$, the coordinates of $B$ are $(6,p)$ and the coordinates of $D$ are $(1,p)$. It is given that the gradient of $AB$ is $-\frac{2}{3}$.

(a) Find the value of $p$.

(b) Find the coordinates of $C$.

(c) Find the area of the triangle formed by the perpendicular bisector of $AB$ and the $x$- and $y$-axes.