### Geometry of Equations

Review question

In the quadrilateral $ABCD$, the points $A$, $B$ and $D$ are at $(3, 3)$, $(0, -1)$ and $(6, 2)$ respectively. The line $BD$ bisects the line $AC$ at right angles at the point $M$. Find the equation of $BD$ and of $AC$.
1. the coordinates of $M$,
2. the coordinates of $C$,
3. the area of the quadrilateral $ABCD$.