Dilation
- Author:
- Rachel Fruin
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.
In your own words, describe dilation.
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.
3) Move the k-value to be 2.
a. How does the coordinate of A’ compare to A? And B’ compare to B? And C’ to C?
b. What happens to the image coordinates when the k-value is 3?
4) With the k-value on 2, click on “Show Segment Lengths.”
a. How does A’B’ compare to AB? How does A’C’ compare to AC? And how does B’C’ compare to BC?
b. How do the segment lengths compare when the k-value is 3?
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.)
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.
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.)
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.
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.)
b. Describe two transformations that make up Composition 1.
9) Uncheck every box. Click on “Composition 2.” Describe the two transformations that make up Composition 2.