## Cartesian Coordinate System

A Cartesian coordinate system in two dimensions is
commonly defined by two axes, at right angles to each other, forming a plane (an

*xy*-plane). The horizontal*axis is normally labeled**x*, and the vertical axis is normally labeled*y*. In a three dimensional coordinate system, another axis, normally labeled*z*, is added, providing 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).An illustration of the Cartesian coordinate system is provided below. The illustration contains four points: (2,3) in green, (−3,1) in red, (−1.5,−2.5) in blue and (0,0), the origin, in yellow.

The point of intersection, where the axes meet, is called the

*origin*normally labeled*O*. The*x*and*y*axes define a plane that is 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, indicate the*x*unit first (abscissa), followed by the*y*unit (ordinate) in the form (*x*,*y*), an ordered pair.The intersection of the two axes creates four regions, called quadrants, indicated by the Roman numerals I (+,+), II (−,+), III (−,−), and IV (+,−). Conventionally, the quadrants are labeled counter-clockwise starting from the upper right ("northeast") quadrant. In the first quadrant, both coordinates are positive, in the second quadrant

*x*-coordinates are negative and

*y*-coordinates positive, in the third quadrant both coordinates are negative and in the fourth quadrant,

*x*-coordinates are positive and

*y*-coordinates negative.