This is an interactive activity to learn about dilations.

1) Click on Dilation with “Center (0, 0).” Use the slider to adjust the “k” value. [br]In your own words, describe dilation.[br][br]2) The scale factor is the ratio of a side length of the image to the corresponding side length of the pre-image. Scale Factor = . “k” is the scale factor of the dilation. Describe which k-values make the dilation an enlargement and which scale factors make the dilation a reduction.[br][br][br]3) Move the k-value to be 2. [br]a. How does the coordinate of A’ compare to A? And B’ compare to B? And C’ to C? [br][br]b. What happens to the image coordinates when the k-value is 3?[br][br]4) With the k-value on 2, click on “Show Segment Lengths.” [br]a. How does A’B’ compare to AB? How does A’C’ compare to AC? And how does B’C’ compare to BC? [br][br]b. How do the segment lengths compare when the k-value is 3?[br][br][br]5) Click on “Lines Through (0, 0) and A, B and C. What is the relationship between the pre-image points, the image points, the center of dilation, and these lines? (Hint: Try dragging the pre-image points to see how the image and lines move. Then adjust the scale factor to see how the image moves.)[br][br][br]6) Uncheck every box, then click on “Dilation with Center E” and “Show Segment Lengths.” You can click and drag point E around. Describe how the placement of the center of dilation affects the transformation.[br]7) Click on “Show Slopes.” How do the slopes of the segments of the pre-image compare to the slopes of the segments of the image? (You can drag points A, B and C around to see if your hypothesis is true.)[br][br][br][br]8) Uncheck every box. Click on “Composition 1.” First semester we talked about the transformations: reflection, rotation and translation. Recall that a composition is a combination of transformations. Dilation is a 4th kind of transformation.[br]a. Which points of the image correspond to the pre-image? (Hint: Drag points A, B and C to find which points correspond to them.)[br][br]b. Describe two transformations that make up Composition 1.[br][br][br]9) Uncheck every box. Click on “Composition 2.” Describe the two transformations that make up Composition 2.