Daily Questions:

1. Daily Questions: • One image of an equilatral triangle is rotated 90d clockwise and a second image is rotated 30d counterclockwise. Describe the relationship between the two images. • Is a rotation always an isometry?

2. Transformations - Dilations Obj: Student will identify a dilation and a scale factor for a polygon.

3. Transformations are changes made to a triangle (or other polygon). • There are several types of transformation: • Translation – move to new location • Dilation – shrink or expand • Reflection – mirror across a point or line • Rotation – turn clockwise or counterclockwise

4. Dilations are very hard to map algebraically, but are intuitively obvious. a’ a b b’ object c image c’

5. Dilations where the image is larger are called enlargements and dilations where the image is smaller are called reductions. a’’ b’’ a c’’ object Image - reduction b a’ c b’ Image - enlargement c’

6. A scale factor describes the change in the object: • Scale factor > 1  bigger image • Scale factor < 1  smaller image a’ a b’ b object Scale factor = 2.0 (image twice as big) c image c’

7. Dilations can have a ‘center of dilation’ that is exactly in the center of the figure. a a’ b’ image b c’ object c

8. Dilations can have the ‘center of dilation’ at a corner or even outside the figure. a a’ b image b’ In this figure, c is the center of dilation and c’ maps onto c. object c’ c