 <p>If you want the intersection of <em>geometric</em> lines, you should take a look at <a href="https://github.com/VincentToups/racket-lib/blob/master/utilities/planar-geometry.rkt" rel="nofollow">this file</a>. It has lots of geometric structures and functions, and you can see the intersection code <a href="https://github.com/VincentToups/racket-lib/blob/master/utilities/planar-geometry.rkt#L386" rel="nofollow">here</a>. Even if your lines use a different structure, the algorithm here should work with some tweaking.</p>