Breaking Bad Symmetries

Point-line configurations in the plane can have many types of symmetries. We will investigate bijections of point-line configurations that preserve a certain structure (automorphisms). Of course, to 'break' these symmetries, we can simply fix all points, but we are interested in the fewest number of points that 'break' all non-trivial automorphisms, called the fixing number. We can view these point-line configurations as matroids and get some more general results.