The Journal of Online Mathematics and Its Applications, Volume 7 (2007)
GeoGebra, Markus Hohenwarter and Judith Preiner

Linear Transformations

With GeoGebra you can also do vector arithmetic. We used this to illustrate a linear transformation by creating two vectors that form the columns of the transformation matrix. In the construction below you can see the column vectors a and b as well as an image of the Statue of Liberty. Drag one of the column vectors with the mouse to change the transformation matrix. The applet will then show you the impact of this linear transformation on the picture of Lady Liberty. You can also drag the picture to another starting position.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and activated. (click here to install Java now)

Editor's note, May 2014: For an HTML5 version of the above applet, click here.

The construction above allows you to explore virtually every possible linear transformation in a plane. Therefore you are able to investigate the characteristics of the matrix itself, as well as special transformations such as rotations by 90°, reflections in the axes, or scaling. GeoGebra enables you to examine the impact of a given matrix on the transformed object, as well as to find the matrix of a special transformation you would like to analyze. Furthermore this construction makes clear that the two column vectors form a new coordinate system for the transformed image.