Monday, September 3, 2012

Free, Semi-free, and Dependent Objects

In GeoGebra, an object may be free, semi-free, or dependent. It is important to understand the differences among the three to perform effective geometric constructions.

This is a Java Applet created using GeoGebra from - it looks like you don't have Java installed, please go to

A free object does not depend on any object. You can move a free object anywhere on the Graphics view. In the figure above, points O and C are free objects. Point O determines the center of the circle which can be placed anywhere, and point C determines its radius.

A semi-free object, on the other hand, depends on one object. Semi-free objects can be moved but with restrictions. In the applet above, point A is a semi-free object. It can move, but only along the circumference of the circle.

Lastly, a dependent object depends on two or more objects. Unlike the other types of objects mentioned above, it cannot be moved by the mouse. For instance, point B above depends on point A and point C. Since it is the midpoint of points A and C, it will only move if point A or point C are moved. 

Exercise: In the applet Exploring Triangles, identify the free, semi-free, and dependent objects.



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