Cartesian coordinate system
Coordinate system using perpendicular axes
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Key Takeaways
- The point where the axes meet is called the origin and has (0, 0) as coordinates.
- The combination of origin and basis forms a coordinate frame called the Cartesian frame .
- More generally, n Cartesian coordinates specify the point in an n -dimensional Euclidean space for any dimension n .
In geometry, a Cartesian coordinate system (UK: , US: ) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, called coordinate lines, coordinate axes or just axes (plural of axis) of the system. The point where the axes meet is called the origin and has (0, 0) as coordinates. The axes directions represent an orthogonal basis. The combination of origin and basis forms a coordinate frame called the Cartesian frame.
Similarly, the position of any point in three-dimensional space can be specified by three Cartesian coordinates, which are the signed distances from the point to three mutually perpendicular planes. More generally, n Cartesian coordinates specify the point in an n-dimensional Euclidean space for any dimension n. These coordinates are the signed distances from the point to n mutually perpendicular fixed hyperplanes.
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