NAME DATE PERIOD 9-6 Study Guide and Intervention

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Lesson 9-6

NAME

DATE

9-6 Study Guide and Intervention

PERIOD

Dilations

Draw Dilations A dilation is a similarity transformation that enlarges or reduces a

figure proportionally. Dilations are completed with respect to a center point and a scale factor.

Example Draw the dilation image of

B'

ABC with center O and r = 2.

B

B

C'

Draw OA , OB , and OC . Label points A , B , and C O

C O

C

so that OA = 2(OA), OB = 2(OB) and

OC = 2(OC). connect the points to draw A B C .

A

A A'

A B C is a dilation of ABC.

Exercises

Use a ruler to draw the image of the figure under a dilation with center S and the scale factor r indicated.

1. r = 2 4

"

# #'

2. r = -21

3

3' $'

4 5'

"'

$

5

3. r = 1

; ;

88

4

9

9

4. r = 3

4

$

5

$'

5'

::

5. r = -23

1

.

1' 3' 3

.'

4

7' 7

8' 8

6. r = 1

( (

''

))

4

, ,

++

Chapter 9

37

Glencoe Geometry

NAME

DATE

PERIOD

9-6 Study Guide and Intervention (continued)

Dilations

Dilations In The Coordinate Plane To find the coordinates of an image after a

dilation centered at the origin, multiply the x- and y-coordinates of each point on the preimage by the scale factor of the dilation, r.

(x, y) (rx, ry)

Example

ABC has vertices A(-2, -2), B(1, -1), and C(0, 2). Find the image

of ABC after a dilation centered at the origin with a scale factor of 2.

Multiply the x- and y-coordinates of each vertex by the scale factor, 2.

(x, y)

(2x, 2y)

A(-2, -2),

A (-4, -4)

B(1, -1)

B (2, -2)

C(0, 2)

C (0, 4)

Graph ABC and its image A B C

y

$ $'

0

x

"

#

#'

"'

Exercises

Graph the image of each polygon with the given vertices after a dilation centered at the origin with the given scale factor.

1. E(-2, -2), F(-2, 4), G(2, 4), H(2, -2); r = 0.5

'

y(

'' ('

0

x

&' )'

&

)

3. A(-2, -2), B(-1, 2), C(2, 1); r = 2

#' y #

0 "

$' $

x

"'

2. A(0, 0), B(3, 3), C(6, 3), D(6, -3), E(3, -3); r = -13

y

#

$

#' $'

"

"' 0

x

&' %'

&

%

4. A(2, 2), B(3, 4), C(5, 2); r = 2.5

y 14

12 10

#'

8

6#

4 2

"

"' $

$'

0 2 4 6 8 10 12 14 x

Copyright ? Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

Chapter 9

38

Glencoe Geometry

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