One very simple linear transformation corresponds to the pure translation of every point by a fixed amount. This has the effect of moving any line to some new line that remains parallel to the original line (and retains the same length). Let e and f be real numbers. Then, the general form of a pure translation by an amount e in the x direction and an amount f in the y direction is given by the assignment

Let this assignment be expressed more compactly by the following single equation:

In the plot below is drawn a modified rectangle to represent a sideways view of a diver.

Translations

Try out different values of e and f in the box below to see how the diver can be translated in the plane.

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This applet shows the side view of a diver. The diver can be translated by entering the values of e and f in the appropriate textfield then pressing "Transform". Note that the transformation will be applied to the current position of the diver. The coordinates of a point on the graph can be obtained by clicking anywhere on the graph. To reset the diver to the initial position, press "Reset". The x and y coordinates will be displayed in the lower left hand side of the applet. To zoom in or zoom out, click the appropriate button.