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DILATIONS

MATH 8

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Dilation

a transformation in which a polygon is enlarged or reduced by a given factor

around a given center point

multiply the dimensions of the pre-image by the factor to get the dimensions

of the image

after a dilation occurs the shapes are no longer congruent, but they are similar

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Scale Factor

image dimensions

pre-image dimensions

the amount by which an image is enlarged or reduced

k

0 < k < 1 🡪

reduction

k = 1 🡪

no dilation

k > 1 🡪

enlargement

shape gets

smaller

shape stays same size

shape gets

LARGER

Dilation Notation

(if the origin is used as center of dilation)

 

 

pre-image

image

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I’ M’

​

​

T’ E’

​

area of T’I’M’E’ is 9

times the area of TIME

each dimension

(length & width)

changed by a scale

factor of 3

Multiply

each by 3

2 square units

18 square units

 

 

 

 

 

 

What do you have to do to get from the pre-image coordinates to the image coordinates?

How many times larger is the image?

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enlargement

k = 4

S’

S’ ( 0 , 4 )

W’ ( 4 , 12 )

A’ ( 12 , 12 )

B’ ( 16 , 4 )

W’

A’

B’

scale factor is greater than 1

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reduction

 

E’ ( 5 , 4 )

P’ ( 5 , 3 )

I’ ( 2 , 3 )

C’ ( 2 , 4 )

E’

P’

I’

C’

scale factor is less than 1

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A figure is shown along with its image after a dilation. Point C is the center of dilation. Determine whether it is an enlargement or reduction, and find the scale factor

distance to the image

 

distance to the pre-image

6

14

 

Reduction

Find a matching

measurement!

scale factor is less than 1

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A figure is shown along with its image after a dilation. Point C is the center of dilation. Determine whether it is an enlargement or reduction, and find the scale factor

distance to the image

distance to the pre-image

10

7

 

Enlargement

leave as improper fraction

scale factor is greater than 1

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A figure is shown along with its image after a dilation. Point C is the center of dilation. Determine whether it is an enlargement or reduction, and find the scale factor

distance to the image

distance to the pre-image

2

6

 

Reduction

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A figure is shown along with its image after a dilation. Point C is the center of dilation. Determine whether it is an enlargement or reduction, and find the scale factor

distance to the image

distance to the pre-image

10

18

 

Reduction

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A figure is shown along with its image after a dilation. Point C is the center of dilation. Determine whether it is an enlargement or reduction, and find the scale factor

distance to the image

distance to the pre-image

16

6

 

Enlargement

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Image B is the result of dilating image A.

Find the scale factor.

B

Find a matching measurement

Pick a matching pair of coordinates

 

 

 

 

 

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