Say we have a collection of n points in the unit square and each point has a line through it. Let delta be the minimal distance from a point in the collection to a line through another point. What is the largest possible delta among all possible collections of points and lines? It is an exercise to show that n^{-1} < delta < n^{-1/2} but improving either of these bounds is not so easy. In 2024, Cohen, Pohoata and myself improved the upper bound to delta < n^{-2/3}. In this talk, I'll present a new simple construction showing that delta > n^{c-1} for some constant c>0. Time permitting, I'll also talk a bit about analogues of this problem over finite fields and in higher dimensions and, in particular, a new upper bound in three dimensions.