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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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slide1

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

Transformations - Dilations

Obj: Student will identify a dilation and a scale factor for a polygon.

slide3

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
slide4

Dilations are very hard to map algebraically, but are intuitively obvious.

a’

a

b

b’

object

c

image

c’

slide5

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’

slide6

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’

slide7

Dilations can have a ‘center of dilation’ that is exactly in the center of the figure.

a

a’

b’

image

b

c’

object

c

slide8

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