Scanning gate experiments on a two-dimensional electron gas in the regime of the classical Hall effect are presented. The Hall resistance is recorded while tuning the local potential by applying a voltage to the metallic tip of a scanning force microscope. In diffusive samples and at zero magnetic field an intriguing Hall resistance pattern arises that is attributed to tip-induced inhomogeneous current flow. Measurements at small, i.e., nonquantizing, magnetic fields reveal an additional Hall resistance pattern due to the tip-induced inhomogeneous electron density in the Hall cross. Deviations of the measurements on higher-mobility samples from expectations based on symmetry arguments are used to distinguish the diffusive from the mesoscopic transport regime. Finite-element-method modeling for the diffusive regime and trajectory calculations for ballistic electrons allow a concise interpretation of the measurements.