[math-fun] Another planar density question

Here's a question similar to Dan's: Let S_n be the set of points in the unit square [0,1]x[0,1] that are expressible as the intersection of two non-parallel lines of the form ax+by=c and dx+ey=f, where a,b,c,d,e,f are integers such that |a|, |b|, |d|, and |e| are all at most n. Do the finite sets S_n approach Lebesgue measure in distribution as n goes to infinity? (If you prefer, take all the lines obtainable by joining two lattice points in [0,n]x[0,n]; then take all the points that can be expressed as the intersection of two such (non-parallel) lines; and then shrink this set of points by a scaling factor of n. That's S_n.) Jim Propp