Ah, Geometry, the great divider. I was fiddling with game development in late high school and the most natural approach to geometric problems for me was to just think in terms of coordinates and disregard the geometric primitives per se. A friend of mine was the same way - just plop a coordinate system, express every point as an algebraic equation and away we do with all these pesky lines on our pages, just nice algebra is left. Then you show it to the teacher and he makes the observation you filled two pages with calculations that can be replaced with one geometric property and the addition of one line to the diagram. Fun times :) .