The $x$- and $y$-axes the $xy$-plane in four right-angle domains which are called the of the plane.  They are numbered going round the origin in anticlockwise direction so that

 $\{(x,\,y)\mid\;x>0,\;y>0\}$

 $\{(x,\,y)\mid\;x<0,\;y>0\}$
The lines $y=\pm x$ have as their slope angles $\pm 45^{\circ}$, thus halving the quadrant angles; they are called the quadrant bisectors.  Cf. angle bisector as locus.