Cartesian Coordinate System

Topics: Analytic geometry, Dimension, Cartesian coordinate system Pages: 3 (697 words) Published: February 3, 2011
Cartesian Coordinate System

-A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Cartesian coordinate system is a way of locating objects in either two- or three-dimensional space by specifying their X(horizontal) position, Y (vertical) position and Z (through) position. It is used in graphics and in positioning text on documents.

-Algebraic equations involving the coordinates of the points lying on the shape. For example, a circle o f radius 2 may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4.

A system or two or three mutually perpendicular axes along which any point can be precisely located with reference to any other point, often referred to as x, y and z coordinates. Relative measure of distance, area and direction are constant throughout the system. The Cartesian coordinate system is named after René Descartes.

The idea of this system was developed in 1637 in two writings by Descartes and independently by Pierre de Fermat, although Fermat used three dimensions, and did not publish the discovery.
Two dimensions

In two dimensions the position of a point P in a plane can be specified by it's distance from two lines intersecting at right angles, called axes. For instance, in Figure 1 two lines intersect each other at right angles in the point 0, the origin. One axis is the line O-X, the other O-Y and any point in the plane can be denoted by two numbers giving it's perpendicular distances from O-X and from O-Y.

A general point P can reached by traveling a distance x along a line O-X, and then a distance y along a line parallel to O-Y. O-X is called the x-axis, O-Y the y-axis, and the point P is said to have Cartesian coordinates (x, y). In the coordinate system shown, as is indicated in the diagram, the...
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