<P> In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space . The order of the coordinates is significant, and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the x-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring . The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the basis of analytic geometry . </P> <P> The simplest example of a coordinate system is the identification of points on a line with real numbers using the number line . In this system, an arbitrary point O (the origin) is chosen on a given line . The coordinate of a point P is defined as the signed distance from O to P, where the signed distance is the distance taken as positive or negative depending on which side of the line P lies . Each point is given a unique coordinate and each real number is the coordinate of a unique point . </P>

Why do we need to specify coordinate axes and an origin
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