Two-dimensional plot of the offsets Δδ vs. Δ α cosδ of the SDSS with respect to the Gaia DR1 positions. In blue we plot the SDSS quasars for which ρ < 200 mas, belonging to the LQAC-3; in green, the SDSS quasars for which ρ < 200 mas, belonging to the DR12Q (LQAC-4–LQAC-3); in yellow, the quasars with ρ > 200 mas belonging to the LQAC-3; in red, the SDSS quasars with ρ > 200 mas belonging tothe DR12Q (LQAC-4–LQAC-3).