The Coordinate Plane, also known as René Descartes' Cartesian Coordinate System, is a system that plots points away from an origin in either two or three dimensions in order to achieve a visual representation of a value that takes either the form of X (where X is for length) and Y (where Y is for height) in two dimensions, or in three dimensions with XYZ (where Z is for width).

the coordinate plane in two dimensions in color with quadrant marks and x and y coordinate

The above coordinate plane shows a two dimensional image (2D) of the way in which these forms can be drawn. Below is the 3D image. In the above image, points can occur anywhere from zero to approaching infinity in four areas that are named quadrants.

 

The above coordinate plane in three dimesions shows how the X, Y, and Z dimensions progress out from their common origin at point (0, 0, 0) where the first zero usually represens the X coordinate ( length) the second zero represents the Y coordinate (height) and the third zero represents the Z coordinate (depth).

3d 8 quadrant graphic

 

Any point in 3d space or in 2d space can be represented by this planar form and the 1d point can be represented as somewhere on the grid. Usually, hash marks or lines are used to visually represent the grid.

Points can occur in eight different areas, as opposed to only four, because the Z dimension adds depth and doubles the amount of space in which a 2D coordinate plane covers, though both forms have sections approaching infinity except now, in 3D, the plane has a larger infinity of possible space to have a point or points within (this notion of a larger infinity was first proposed by Gregor Cantor).

The above graphic shows how the lines can be drawn to mimic curvature along the four quadrants where the curve is that of a perfect circle's edge.



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