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In geometry, a Cartesian coordinate system (UK: / k ɑːr ˈ t iː zj ə n /, US: / k ɑːr ˈ t iː ʒ ə n /) 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 ...
Special cases are called the real line R 1, the real coordinate plane R 2, and the real coordinate three-dimensional space R 3. With component-wise addition and scalar multiplication, it is a real vector space. The coordinates over any basis of the elements of a real vector space form a real coordinate space of the same dimension as that of the ...
Another common coordinate system for the plane is the polar coordinate system. [7] A point is chosen as the pole and a ray from this point is taken as the polar axis. For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ (measured counterclockwise from the axis to the line).
Illustration of a Cartesian coordinate plane. Four points are marked and labeled with their coordinates: (2,3) in green, (−3,1) in red, (−1.5,−2.5) in blue, and the origin (0,0) in purple. In analytic geometry, the plane is given a coordinate system, by which every point has a pair of real number coordinates.
For a geographic coordinate system of the Earth, the fundamental plane is the Equator. Astronomical coordinate systems have varying fundamental planes: [2] The horizontal coordinate system uses the observer's horizon. The Besselian coordinate system uses Earth's terminator (day/night boundary). [3] This is a Cartesian coordinate system (x, y, z).
The Earth-centered, Earth-fixed coordinate system (acronym ECEF), also known as the geocentric coordinate system, is a cartesian spatial reference system that represents locations in the vicinity of the Earth (including its surface, interior, atmosphere, and surrounding outer space) as X, Y, and Z measurements from its center of mass.
A Euclidean plane with a chosen Cartesian coordinate system is called a Cartesian plane. The set R 2 {\displaystyle \mathbb {R} ^{2}} of the ordered pairs of real numbers (the real coordinate plane ), equipped with the dot product , is often called the Euclidean plane or standard Euclidean plane , since every Euclidean plane is isomorphic to it.
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