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The $x$- and $y$-axes divide the $xy$-plane in four right-angle domains which are called the quadrants 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.

Defines:

1st quadrant, 2nd quadrant, 3rd quadrant, 4th quadrant

Related:

RightAngle, ConvexAngle, Octant

Synonym:

quarter-plane

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

51N20*no label found*

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