The Coordinate System Transformations applet teaches several concepts. The first is how a transformation applied to a coordinate system affects the axes of that coordinate system. Second, this applet shows how looking at only a very small portion of any curve produces a straight line (linear approximation) of that curve. Finally, this applet shows how a transformation of the coordinate system affects any objects within that coordinate system.
Undergraduate students with an interest in math and graphics. Requires only basic algebra and trigonometry.
The top two windows show an image of the current graph and a rectangle which shows the bounds of the magnified areas located below. The rectangle can be moved either by clicking on a point on the left graph or by dragging the rectangle around the graph. Keep in mind that the rectangle shown on the left is not necessarily a rectangle on the right due to the transformation. The rectangle cannot be moved by clicking on the right graph since not every point on the right graph has a distinct point on the left graph.
The equation used for the transformation can be chosen from the pop-up list on the right, and the magnification can be changed by dragging the slider. Finally, it is possible to draw on the left-hand graph by dragging the mouse around within the magnified area. The resulting points will be drawn on the right-hand graph. Keep in mind that, due to the transformation, not every point on the left-hand graph has a visible point on the right-hand graph. A straight line can also be drawn by using the middle or right mouse button, or by shift-clicking and dragging within the magnified area.