When a straight conductor carries a current along the z-axis the magnetic field produces in XY plane.
Here, all the four points are located on either X or Y axis at distance of magnitude 'a' from origin. Thus all four points have magnetic fields of the same magnitude but in different directions. Also, A and C are located on positive and negative X axis respectively hence, the magnetic fields at A and C are in opposite directions. While A and B are located on positive x axis and negative Y axis hence, the magnetic fields at A and B are mutually perpendicular to each other.