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Cartesian coordinates (rectangular coordinates)

Cartesian coordinates, also called rectangular coordinates, provide a method of rendering graphs and indicating the positions of points on a two-dimensional (2D) surface or in three-dimensional (3D) space. The scheme gets its name from one of the first people known to have used it, the French mathematician and philosopher René Descartes (1596-1650). Cartesian coordinates are used to define positions on computer displays, in 3D models and virtual reality (VR) renderings. The coordinate system is also employed in mathematics, physics, engineering, navigation, robotics, economics and other sciences.

The Cartesian plane consists of two perpendicular axes that cross at a central point called the origin. Positions or coordinates are determined according to the east/west and north/south displacements from the origin. The east/west axis is often called the x axis, and the north/south axis is called the y axis. For this reason, the Cartesian plane is also known as the xy -plane. The x and y axes are linear number lines, meaning that each division on a given axis always represents the same increment. However, the increments on different axes can differ. For example, in the illustration at left below, each increment on the x axis might represent 2 units, while each increment on the y axis represents 5 units. Points or coordinates are indicated by writing an opening parenthesis, the x value, a comma, the y value, and a closing parenthesis in that order. An example is ( x,y ) = (2,-5). The origin is usually, but not always, assigned the value (0,0).

 

Cartesian three-space, also called xyz -space, has a third axis, oriented at right angles to the xy plane. This axis, usually called the z axis, passes through the origin of the xy -plane. Positions or coordinates are determined according to the east/west ( x ), north/south ( y ), and up/down (z) displacements from the origin. As is the case with the x and y axes, the z axis is a linear number line. For example, in the illustration at right above, each increment on the x axis might represent 5 units, each increment on the y axis 10 units, and each increment on the z axis 2 units. Points or coordinates are indicated by writing an opening parenthesis, the x value, a comma, the y value, another comma, the z value, and a closing parenthesis in that order. An example is ( x,y,z ) = (5,-10,-4). The origin is usually, but not always, assigned the value (0,0,0).

Other coordinate systems include semilog coordinates, log-log coordinates, polar coordinates, cylindrical coordinates, spherical coordinates and azimuth and elevation.

Khan Academy provides an introduction to the coordinate plane:

This was last updated in October 2016

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informative but short.....
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How do we find the angle between the vector components of two vectors
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