HONORS GEOMETRY 9.6. Dilations Day One. Do Now: What is an isometry? Discuss with a neighbor (no need to write anything down)

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Presentation transcript:

HONORS GEOMETRY 9.6. Dilations Day One

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

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

Dilations:

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?

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.

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

Example One (Continued):

Example Two:

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

You Try!

Example Three: What’s the scale factor?

Example Four: What’s the scale factor?

You Try!

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?

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?

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 millimeter wide print (X’Y’) from a 35 millimeter wide negative (XY).

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.

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