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The Cartesian Coordinate System

Updated on February 28, 2008


Many relationships between two variables are shown by graphs. Some of the many examples are blood pressure and time , profit and production, distance and time, ACT score and raw score on the test , area and radius of a circle. A two-dimensional system is used to draw graphs. The rectangular coordinate system presented here is the most commonly used method for the plane. This present method was invented by French mathematician and philosopher named Rene Descartes (1596-1650) , and it is called the "cartesian" or rectangular coordinate system for the plane.

To set up this system we first draw two perpendicular number lines in a plane. The unit of length of these lines may be the same or different . The two lines are called the coordinate axes . The horizontal line is called the X-axis. It has positive direction to the right and negative direction to the left. The vertical line is known as the Y-axis. It has positive direction upward and negative direction downward. Their point of intersection is known as the origin. The coordinate axes divide the plane into four parts called "quadrants", and they maybe numbered I, II, III, IV in a counterclockwise direction.

Given that a and b are real numbers, then (a, b ) is called an ordered pair . Everypolnt in a coordinate plane can be assigned a specific ordered pairs of numbers We assign to P the ordered pair (a, b). a is called the abscissa. or X-coordinate and b is called the ordinate or Y-coordinate. The point (a, b) is "a " unit away from the Y-axis "b' unit away from the X-axis. We locate the point P(a, b) on the plane by drawing a vertical line through "a" on the X-axis and a horizontal line through "b"on the Y-axis. The point is found at the intersection of these rwo lines.

The table below shows the corresponding sign of the abscissa and the ordinate depending upon which quadrant the point is located.


Abscissa +

Ordinate +



Abscissa -

Ordinate +


Quadrant III

Abscissa -

Ordinate -


Quadrant IV

Abscissa +

Ordinate -



Paul K. Rees


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      8 years ago

      i agree with this


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