We explore the use of centroid coordinates as a means to identify the "locations" of electron-proton bremsstrahlung hard X-ray sources in solar flares. Differences between the coordinates of the electron and photon centroids are derived and explained. For electron propagation in a collision-dominated target, with either a uniform or an exponential density profile, the position of the electron centroid can be calculated analytically. We compare these analytic forms to data from a flare event on 2002 February 20. We first spectrally invert the native photon visibility data to obtain "electron visibilities," which are in turn used to construct electron flux images at various electron energies E. Centroids of these maps are then obtained by straightforward numerical integration over the electron maps. This comparison allows us to infer the density structure in the two compact sources visible, and we discuss the (somewhat unexpected) results thus obtained.