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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 ?. Transformations - Dilations.
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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?
Transformations - Dilations Obj: Student will identify a dilation and a scale factor for a polygon.
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
Dilations are very hard to map algebraically, but are intuitively obvious. a’ a b b’ object c image c’
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’
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’
Dilations can have a ‘center of dilation’ that is exactly in the center of the figure. a a’ b’ image b c’ object c
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