I was reading about Triangle Interiors on Wolfram Alpha:
http://mathworld.wolfram.com/TriangleInterior.html
and they have a simple equation: $$\mathbf{v} = \mathbf{v}_0 + a\mathbf{v}_1 + b\mathbf{v}_2,$$ and then they solve for $a$ and $b$, but I wasn't sure about the steps of how they went about doing that.
My algebra is rusty...