Internet Resources for the Calculus Student - Topics in Precalculus

Cartesian Coordinates

A Cartesian Coordinate System identifies each point in a plane with an ordered pair of real numbers (called the coordinates of the point) by taking the directed distance of the point from each of two given perpendicular straight lines (called the axes). Typically one axis (usually called the x-axis) is placed horizontally with positive direction to the right, and the other (usually called the y-axis) is placed vertically with positive direction up. Distance from each axis is measured along the other one, so the distance from the y-axis is called the x-coordinate and vice-versa. The coordinates of a point are listed in brackets with the x-coordinate (also called the Abscissa) first, and the y-coordinate (also known as the Ordinate) second. The point where the axes meet is called the Origin and has coordinates (0,0). Points with positive x-coordinate are in the Right Half Plane and those with negative x-coordinate are in the Left Half Plane. And similarly positive and negative y-values correspond to the Upper and Lower Half Planes respectively.

Well that wasn't quite a thousand words, but a picture would certainly be better!
 



If you have a Java-enabled browser, then you can use our Graph Explorer to see how the cordinates of a point vary as it is moved about.  (Any Computer Algebra System or Graphing Calculator might do as well of course but the specific instructions would be a bit different.)

For guidance through a more detailed exploration you can work through our on-line lab on Cartesian Coordinates.

Here are some more links that you might find useful.

If you have come across any other good web-based illustrations of these and related concepts, please do let us know and we will add them here.