Let $A = (0, 0),$ $B = (1, 2),$ $C=(3, 3),$ and $D = (4, 0).$ Quadrilateral $ABCD$ is cut into two pieces with the same area by a line passing through $A$. What are the coordinates of the point where this line intersects $\overline{CD}$?
We can quickly figure out that the line through A must have slope 1/2. So y = x/2, and the line CD is y = -3x + 12. Solving these equations, you can find (x,y) = (24/7,12/7).
+230 
