In case of translational symmetry in some charge configuration, why is it must that potential remains constant along that line?

When there is translational symmetry along a charge configuration why is it must that potential always remains constant along that line, it may be said that electric field will remain constant at every point on that line in that configuration, because from upon taking 2 distinct points we observe the configuration to be the same at both of them. however how can the same be said about potential with some defined origin. or rephrasing my question if there is translational symmetry in a charge configuration about some axis then why is must that the electric field must be perpendicular to that axis.