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Linear Transformations in the Plane

Tool for showing the linear transformation of a region. User controls the four points of the region and the \(2 \times 2\) transformation matrix.

Average: 4 (2 votes)
Steve Levandosky
David Strong
College of the Holy Cross website
Steve Levandosky
Format Other: 
Java may need to be enabled in the Java Console

Comments's picture

The user enters a \(2\times2\) matrix (using sliders for the entries), draws one or more lines, rectangles, circles, and/or freehand curves on the left-hand set of axes (choosing the desired type(s) to draw from a drop-down menu), and sees the result of applying the transformation to the drawn figures on the right-hand set of axes. The matrix can be changed without erasing the figures, so it is easy to see the effect of increasing or decreasing a particular matrix entry. Drawn figures can be erased in reverse order or all at once. The default matrix is an identity matrix. A reset button returns the matrix to its default value. The windows can't be zoomed in or out, so it's possible for the result of a transformation to fall outside the window and therefore out of view. There is also no provision for translating the image to bring it into view. Nevertheless, this applet allows for experimentation with simple linear transformations to develop intuition on how they act.

Anonymous's picture

The ability to draw anything is useful.