A coordinate system is a metric geometry (a geometry where distance can be measured) where the location of a point is identified by one or more coordinates.^{[1]} The coordinates of a point is a set of numbers that indicate a position relative to an origin. In a coordinate system, points can be plotted and graphs can be made. In a coordinate system, visual representation of equations and other mathematical objects can be created. Two of the most commonly used coordinate systems are the Cartesian coordinate system and the polar coordinate system.
 
Manipulative 1: Cartesian coordinate system. Click on the green point and drag it to change the figure. Double click on the figure to launch an independent application. 
The most commonly used coordinate system is the Cartesian coordinate system.^{[2][3]} It is named after French mathematician René Descartes, who formalized the concepts of coordinate systems in his book, La Géométrie. A Cartesian coordinate system can also be called a rectangular coordinate system.
In a 2dimensional Cartesian coordinate system, there are 2 axes set in a plane. One axis is vertical and the other axis is horizontal. The plane is called a Cartesian plane or coordinate plane. The horizontal axis is usually called the xaxis and the vertical axis is usually called the yaxis The point where the two axes intersect is called the origin. To make discussion easier, the coordinate plane is divided into four quarters, each called a quadrant. The upperright quadrant is called Quadrant I, the upper left quadrant is called Quadrant II, the lower left quadrant is called Quadrant III, and the lower right quadrant is called Quadrant IV.
Corresponding to the xaxis and yaxis is an ordered pair of numbers that is the coordinates. The coordinates tell the location of a point. For example, in the ordered pair of numbers (x_{0},y_{0}), x_{0} tells the distance from the origin parallel to the xaxis and is called the xcoordinate. y_{0} tells the distance from the origin parallel to the xaxis and is called the ycoordinate.
To plot a point such as (1,1), start from the origin, then move 1 unit to the right (positive direction) along the xaxis, and 1 unit up parallel for the yaxis. See figure 1.

In a polar coordinate system the location of a point is defined by an angle, and a radius or magnitude.^{[4]} To plot the point (2,60°), find the rotation of 60°, then move 2 units out from the origin. See figure 2. 

Word processing programs use a coordinate system with the origin in the upper left hand corner for languages that are read from left to right. The horizontal coordinate increases to the right. The vertical coordinate increase downwards. Figure 1 shows the coordinate system in Open Office Writer 3.2.0. For languages that are read from right to left, the origin is on the right and the horizontal increase goes from right to left. In publishing, the unit for the horizontal and vertical axes are picas. Each pica measures 1/6^{th} of an inch. 
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