## What Is the Cartesian Coordinate System?

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The mathematical system that indicates the position of each point in the system by its distance from two perpendicular lines, is known as the Cartesian coordinate system.  The two lines intersect at right angles at a point called the origin.  The two lines that intersect to make the coordinate plane are called the x-axis and the y-axis.  The coordinates of the points on the plane have special names too.  The x coordinate is called the abscissa and the y coordinate is called the ordinate. The origin is the point has the coordinates (0,0).

Whenever you graph an equation, you are using the work of René Descartes. René Descartes is the French mathematician who is credited with inventing the Cartesian coordinate plane.  His surname, Descartes, means some charts or some maps.  There is a legend in which math historians claim  that Descartes thought of the coordinate system while lying in bed. Descartes is supposed to have noticed a fly walking across the ceiling of his bedroom. While watching the fly, Descartes began to think of how to describe the fly’s path without actually tracing its path. His thoughts about describing a path by mathematical means led to his invention of coordinate geometry.

Descartes expressed a line as an equation using letters of the alphabet to represent variables and constants.  Those at the end of the alphabet, x, y, and z were used for variables and those from the beginning, such as a, b, and c, he used for constants.  This is a practice that continues today.

The x-axis and y-axis are two lines that create the coordinate plane.  The x-axis is a horizontal line and the y-axis is a vertical line. When one first learns to graph equations by plotting points on the plane, it is hard to remember which line is which.  If you say this phrase, “x to the left and y to the sky,”* you can hear the “rhymes”. X rhymes with left and Y rhymes with sky.  Remember the x-axis is really a horizontal line so it runs to both the right and the left.  The y-axis is a vertical line so it runs up and down.  When you draw the two lines, it is important to put arrows at the ends of each axis to indicate that these lines go on forever.

We use Cartesian coordinates to locate a point in space. This is done by giving its relative distance from the axes or perpendicular intersecting lines. In coordinate geometry, all points, lines, and figures are drawn in a coordinate plane. By referring to the two coordinate axes, any point, line, or figure may be precisely located.

In Descartes's system, the first coordinate value is the x-coordinate or abscissa and it tells where the point is located along the x-axis. The second coordinate value is the y-coordinate or ordinate and it tells the position of the point along the vertical or y-axis. A point with coordinates (3, -1) is located three units to the right of the origin and then one unit below the vertical position of the origin.

A linear equation represents a straight line and this line can be drawn on a coordinate plane.  Every point on a line has coordinate values that satisfy a specific mathematical equation.  More complex equations are used to represent circles, ellipses and curved lines.  The Cartesian coordinate system combines algebra and geometry, and is a universal system for locating points.  Applications include computer graphics, animation, and GPS [Global Positioning Systems].

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