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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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## PowerPoint Slideshow about 'Daily Questions:' - mikko

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Presentation Transcript

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.

• 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