# Two-dimensional coordinate system

The modern Cartesian coordinate system in two dimensions (also called a
rectangular coordinate system) is commonly defined by two axes, at right angles
to each other, forming a plane (an *xy*-plane). The horizontal axis is labeled *x*,
and the vertical axis is labeled *y*. In a three-dimensional coordinate system,
another axis, normally labeled *z*, is added, providing a sense of a third
dimension of space measurement. The axes are commonly defined as mutually
orthogonal to each other (each at a right angle to the other). All
the points in a Cartesian coordinate system taken together form a so-called Cartesian plane.

The point of intersection, where the axes meet, is called the origin normally
labeled **O**. With the origin labeled O, we can name the *x-*axis O_{x} and the *y*-axis
O_{y}. The *x* and *y* axes define a plane that can be referred to as the *xy*-plane.
Given each axis, choose a unit length, and mark off each unit along the axis,
forming a grid. To specify a particular point on a two dimensional coordinate
system, you indicate the x unit first (abscissa), followed by the y unit
(ordinate) in the form (x,y), an ordered pair. In three dimensions, a third *z* unit (applicate) is added, (*x*,*y*,*z*).

The choices of letters come from the original convention, which is to use the latter part of the alphabet to indicate unknown values. The first part of the alphabet was used to designate known values.

An example of a point P on the system is indicated in the picture below using the coordinate (5,2).

In the two-dimensional Cartesian coordinate system, a point P in the xy-plane
is represent by a tuple of two components (*x*,*y*).

*x*is the signed distance from the*y*-axis to the point P, and*y*is the signed distance from the*x*-axis to the point P.

In the three-dimensional Cartesian coordinate system, a point P in the xyz-space is represent by a tuple of three components (x,y,z).

*x*is the signed distance from the*yz*-plane to the point P,*y*is the signed distance from the*xz*-plane to the point P, and*z*is the signed distance from the*xy*-plane to the point P.

The arrows on the axes indicate that they extend forever in the same direction (i.e. infinitely). The intersection of the two x-y axes creates four quadrants indicated by the Roman numerals I, II, III, and IV. Conventionally, the quadrants are labeled counter-clockwise starting from the northeast quadrant. In Quadrant I the values are (x,y), and II:(-x,y), III:(-x,-y) and IV:(x,-y).

Quadrant | x values | y values |
---|---|---|

I | > 0 | > 0 |

II | < 0 | > 0 |

III | < 0 | < 0 |

IV | > 0 | < 0 |

**See also**

2D | Two-dimensional coordinate system |

3D | Three-dimensional coordinate system |

Angle | Definition of an angle |

Axis | Definition of Cartesian axis |

Cartesian geometry | What is Cartesian geometry? |

Coordinate system | Definition of coordinates |

Curve | Definition of a curve |

Distance | Definition of distance |

Euclidean geometry | What is Euclidean geometry? |

Geometry | Definition of geometry |

Length | Definition of length |

Line | Definition of a line |

Origin | Definition of origin in a Cartesian coordinate system |

Perspective projection | Definition of perspective projection |

Planar homography | Definition of planar homography |

Plane | Definition of a plane |

Point | Definition of a point |

Point (kinematics) | Definition of a point (kinematics) |

Projective geometry | What is projective geometry? |

Segment (kinematics) | Definition of a segment (kinematics) |

Vanishing points | Definition of vanishing points and vanishing lines in perspective projection |

Vector | Definition of a vector |