Cartesian Coordinate System

The two-dimensional Cartesian coordinate is defined by two axes, at right angles to each other, forming a plane (the xy-plane). The horizontal axis is labeled x (sometimes called abscissa), and the vertical axis is labeled y (sometimes called ordinate). The point of intersection, where the axes meet, is called the origin, which is normally labeled O. To specify a particular point on a two dimensional coordinate system, you indicate the x unit first (abscissa), followed by the y unit (ordinate) in the form [x,y].

The two intersecting axes create four quadrants which are numerated counter-clockwise by Roman literals. For example, the point P1 in the figure below lies in the first quadrant, the point P2 is located in the third quadrant.

The distance between a point P and the origin O calculates from the Pythagorean theorem.

The distance between two points P1 and P2 calculates the same way as:

source: creativecommons

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