27 lines
1.5 KiB
Markdown
27 lines
1.5 KiB
Markdown
# Cartesian Coordinate System
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**A two-dimensional coordinate system in which every point is uniquely identified by a pair of signed distances to a pair of perpendicular lines.**
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![[CartesianCoordinateSystem.svg]]
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_A Cartesian coordinate plane_
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The **Cartesian coordinate system** is a two-dimensional coordinate system that uniquely identifies each point in two-dimensional Euclidean space using an _ordered pair of signed distances_ to an ordered pair of fixed perpendicular lines known as the _axes_.
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The intersection of the two axes is known as the _origin_ and is defined as .
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## Higher dimensions
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The Cartesian coordinate system can be generalised to _any_ -dimensional Euclidean space.
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In an -dimensional Euclidean space, points are specified with an ordered set of _signed distances_ to an ordered set of fixed perpendicular _dimension hyperplanes_ instead.
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![[CartesianCoordinateSystem3D.svg]]
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_The Cartesian coordinate system in three dimensions with the - Cartesian coordinate plane embedded_
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## Notation
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In two-dimensional Cartesian coordinates, the horizontal and vertical axis are often denoted as the _-axis_ and the _-axis_, respectively. Extending into three dimensions, the third axis is often denoted the _-axis_.
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The coordinates themselves are referred to, in order, as the , , and coordinates. The and coordinates may also be referred to as the _abscissa_ and the _ordinate_, respectively. Generic coordinates are thus notated as or .
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The axes and coordinates may also be denoted using _subscripts_, as in , which is extendable to any -dimensions. |