A motor vehicle headlight has a single light source and a single reflector which receives the light from the source, and which is tripod mounted on three bearing points defining the three apices of a triangle. The headlight has controlled displacement means for selectively displacing at least one of these bearing points in straight line movement. The controlled displacement means comprise a single beam switching device for displacing one of the three bearing points into one of only two discrete positions, namely a first position corresponding to a dipped beam and a second position, higher than the first position, corresponding to a main beam.