Summary: In this paper we construct a compactification of the moduli space \(B^*_ n=({\mathbb{P}}^ n_ 2\setminus \Delta)/PGL(3)\) of n-point configurations in the plane in general position modulo linear transformations. This compactification \(B_ n\) is an analogue to the space of n-pointed trees of projective lines and a generalization of a compactification of orbit spaces of more general group actions. We relate the fibres of the universal n-point configuration \(F_ n\to B_ n\) to schemes associated with the Bruhat-Tits building and give explicit descriptions in the cases \(n=5\) and \(n=6\).