# quadrant

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

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

is the first quadrant,

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

the second quadrant, and so on.

Naturally, one can speak of the quadrants of the complex plane, too.

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.

 Title quadrant Canonical name Quadrant Date of creation 2014-12-16 22:42:51 Last modified on 2014-12-16 22:42:51 Owner Mathprof (13753) Last modified by pahio (2872) Numerical id 14 Author Mathprof (2872) Entry type Definition Classification msc 51N20 Synonym quarter-plane Related topic RightAngle Related topic ConvexAngle Related topic Octant Defines 1st quadrant Defines 2nd quadrant Defines 3rd quadrant Defines 4th quadrant