Coordinate Systems and Axes

A coordinate system quantizes the plane and the location of objects on it. A coordinate system is defined by an origin, a scale, and a grid form or shape. The origin of a coordinate system is the point or the position at the center of the coordinate axes. The scale of a coordinate system determines the size of each unit on an axis. The grid form of a coordinate system determines how coordinates are measured. In the most common form—a square coordinate system—coordinates are indicated as horizontal and vertical distances from the origin, measured in the same unit scale. Rectangular coordinate systems are like square coordinate systems in that they measure coordinates horizontally and vertically from the origin, but they have separate scales for each axis. Finally, a polar coordinate system measures coordinates by a distance and a direction from the positive horizontal axis, rather than by horizontal and vertical distance from the origin.

The default coordinate system has an origin point in the center of your screen and a unit point at (1, 0). Drag the origin to relocate the coordinate system and drag the unit point to change its scale.

Many of Sketchpad’s analytic measurements—such as Coordinates, Equation, and Slope—and all of the plotting commands—such as Plot Points, Plot As (x, y), or Plot New Function—are defined in reference to a coordinate system. If you do not create a new coordinate system before using these commands, they will create a default square coordinate system for you, and their results will be defined in terms of that coordinate system.

To create a coordinate system:

· Choose Define Coordinate System from the Graph menu. Depending on the objects you’ve selected, there are several different ways this command constructs the coordinate system.

· Measure or plot a quantity that requires a coordinate system, such as Coordinates, Coordinate Distance, Slope, Equation, or Plot Points. If you don’t already have a coordinate system, any of these commands will create one.

Subtopics:
Modifying a Coordinate System
Using Coordinate Systems
Multiple Coordinate Systems
How To Construct a Geoboard