(This activity was modified from an original activity created by Shannon Rush.)[br][br]A [b]dilation [/b]is a transformation in which a figure is enlarged or reduced with respect to a given point. The point is called the "[b]center of dilation[/b]." [br][br]The [b]scale factor[/b] (often written as [i]k[/i]) is the ratio of the lengths of the corresponding sides of the image and the original. [br] [br]In the GeoGebra applet below, click the "Dilation" button to show the dilation of the triangle with respect to the point. Use the slider to change the scale factor. Move the points of the original triangle. Essentially play with all the factors involved! As you do, pay attention to the effects on the points, segments, and angles. [br][br][b][u]Discuss with your table partners:[br][br][/u][/b](1) Why do you think we use [i]k[/i] to represent the scale factor, and not some other variable (such as [i]m[/i], [i]s[/i], or [i]d[/i])?[br][br](2) How do the angles in the pre-image and dilated image compare to each other?[br][br](3) How do the side lengths in the pre-image and dilated image compare to each other?[br][br]

[b][u]Algebraic Rules[/u][/b][br][br]Now, let's observe the change in the ordered pairs. Think back to the "Blue Point Rule" activity, where you used casework to determine the algebraic rule for a transformation.[br][br]Set "d = 3" in the applet above. On a piece of paper, create a table with the pre-image points (A, B, C) and the image points under the dilation (A', B', C'). [br][br]Can you and your table partners determine an algebraic rule that describes this transformation?[br][br][b][u]Side Length Comparison[/u][/b][br][br]Now, use the GeoGebra sketch below and the provided table to help you compare figures' side lengths.[br][br]In cell B1, type: =A'B'/AB[br][br]In cell B2, type: =B'C'/BC[br][br]In cell B3, type:  =A'C'/AC[br][br]Then, use the arrow tool to change the scale factor and the vertices of the triangle.[br][br]What do you notice?[br][br][b][u]Scale Factor Observations[br][/u][/b][br]There are specific things that occur with certain types of scale factors. Try out each situation and discuss what happens with your table group.[br][br]a) When the scale factor is greater than 1, how does the image compare to the original? [br][br]b) When the scale factor is 1, how does the image compare to the original? [br][br]c) When the scale factor is between 0 and 1, how does the image compare to the original?[br][br]d) When the scale factor is less than 0 (negative), how does the image compare to the original? [br][br]

Original activity by Shannon Rush.[br][br]Edited by Dr. Lockley.