Editing Cartesian coordinate system (section)

===Two dimensions===
{{Further|Two-dimensional space}}

A Cartesian coordinate system in two dimensions (also called a '''rectangular coordinate system''' or an '''orthogonal coordinate system'''<ref name=":0" />) is defined by an [[ordered pair]] of [[perpendicular]] lines (axes), a single [[unit of length]] for both axes, and an orientation for each axis. The point where the axes meet is taken as the origin for both, thus turning each axis into a [[number line]]. For any point ''P'', a line is drawn through ''P'' perpendicular to each axis, and the position where it meets the axis is interpreted as a number. The two numbers, in that chosen order, are the ''Cartesian coordinates'' of ''P''. The reverse construction allows one to determine the point ''P'' given its coordinates.

The first and second coordinates are called the ''[[abscissa]]'' and the ''[[ordinate]]'' of ''P'', respectively; and the point where the axes meet is called the ''origin'' of the coordinate system. The coordinates are usually written as two numbers in parentheses, in that order, separated by a comma, as in {{nowrap|(3, −10.5)}}. Thus the origin has coordinates {{nowrap|(0, 0)}}, and the points on the positive half-axes, one unit away from the origin, have coordinates {{nowrap|(1, 0)}} and {{nowrap|(0, 1)}}.

In mathematics, physics, and engineering, the first axis is usually defined or depicted as horizontal and oriented to the right, and the second axis is vertical and oriented upwards. (However, in some [[computer graphics]] contexts, the ordinate axis may be oriented downwards.) The origin is often labeled ''O'', and the two coordinates are often denoted by the letters ''X'' and ''Y'', or ''x'' and ''y''. The axes may then be referred to as the ''X''-axis and ''Y''-axis. 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.

A [[Euclidean plane]] with a chosen Cartesian coordinate system is called a '''{{vanchor|Cartesian plane}}'''. In a Cartesian plane, one can define canonical representatives of certain geometric figures, such as the [[unit circle]] (with radius equal to the length unit, and center at the origin), the [[unit square]] (whose diagonal has endpoints at {{nowrap|(0, 0)}} and {{nowrap|(1, 1)}}), the [[unit hyperbola]], and so on.

The two axes divide the plane into four [[right angle]]s, called ''quadrants''. The quadrants may be named or numbered in various ways, but the quadrant where all coordinates are positive is usually called the ''first quadrant''.

If the coordinates of a point are {{nowrap|(''x'', ''y'')}}, then its [[distance from a point to a line|distances]] from the ''X''-axis and from the ''Y''-axis are {{abs|''y''}} and {{abs|''x''}}, respectively; where {{abs}} denotes the [[absolute value (algebra)|absolute value]] of a number.

{{Anchor|Cartesian coordinates in three dimensions}}