1. HONORS GEOMETRY 9.6. Dilations Day One

2. Do Now: What is an isometry? Discuss with a neighbor (no need to write anything down)

3. Today? So far we have… Rotations Reflections Translations NOW? Dilations!

4. Dilations:

5. Easier Way? Dilation makes objects bigger or smaller. Realize– this means dilations will end up with similar shapes (not congruent like before) Is a dilation an isometry?

6. Within a coordinate plane To find the coordinates of an image after a dilation centered at the origin, multiply the x- and y-coordinates of each point on the preimage by the scale factor of the dilation, k.

7. Example One: Dilate Triangle STU by a factor of 2. Use the origin as the center of dilation

8. Example One (Continued):

9. Example Two:

11. Realize… If a scale factor is _____________ the object will be larger. If a scale factor is ________________ the object will get smaller.

12. You Try!

13. Example Three: What’s the scale factor?

14. Example Four: What’s the scale factor?

15. You Try!

16. Example Five: To create the illusion of a “life-sized” image, puppeteers sometimes use a light source to show an enlarged image of a puppet projected on a screen or wall. Suppose that the distance between a light source L and the puppet is 24 inches (LP). To what distance PP' should you place the puppet from the screen to create a 49.5-inch tall shadow (I'M') from a 9-inch puppet?

17. Example Six: Suppose you have a similar situation with the puppet and light source. The distance between the light source L and the puppet is 30 inches (LP). To what distance should you place the puppet from the screen to create a 54-inch tall shadow (I'M') from a 6-inch puppet?

18. You Try! To create different sized prints, you can adjust the distance between a film negative and the enlarged print by using a photographic enlarger. Suppose the distance between the light source C and the negative is 45 millimeters (CP). To what distance PP’ should you adjust the enlarger to create a 227.5 millimeter wide print (X’Y’) from a 35 millimeter wide negative (XY).

19. Practice Problems Try some on your own/in your table groups. As always don’t hesitate to ask me questions and/or talk to your tablemates– they are your greatest resource.

20. Exit Ticket: