Given a finite set of straight line segments S in R^{2} and some k\in N, is there a subset V of points on segments in S with \vert V \vert \leq k such that each segment of S contains at least one point in V? This is a special case of the set covering problem where the family of subsets given can be taken as a set of intersections of the straight line segments in S. Requiring that the given subsets can be interpreted geometrically this way is a major restriction on the input, yet we have shown that the problem is still strongly NP-complete. In light of this result, we studied the performance of two polynomial-time approximation algorithms which return segment coverings. We obtain certain theoretical results, and in particular we show that the performance ratio for each of these algorithms is unbounded, in general.