FeatureLesson

GeometryGeometry

LessonMain

Tell what type(s) of symmetry each figure has.

1. D

2. O

reflectional: horizontal line of symmetry

reflectional: horizontal and vertical lines of symmetry; rotational: point symmetry

Draw each figure and all its lines of symmetry.

3. isosceles right triangle 4. rhombus that is not a square

Lesson 9-4

SymmetrySymmetry

5. The star below appears on the United States flag. If the star has line symmetry, sketch it and draw the line(s) of symmetry. If it has rotational symmetry, state the angle of rotation.

72° rotational symmetry

Lesson Quiz

9-5

FeatureLesson

GeometryGeometry

LessonMain

FeatureLesson

GeometryGeometry

LessonMain

FeatureLesson

GeometryGeometry

LessonMain

Lesson 9-5

DilationsDilations

9-5

A dilation is a transformation that changes the size of a figure but not the shape. The image and the preimage of a figure under a dilation are similar.

FeatureLesson

GeometryGeometry

LessonMain

Lesson 9-5

DilationsDilations

9-5

FeatureLesson

GeometryGeometry

LessonMain

Lesson 9-5

DilationsDilations

9-5

FeatureLesson

GeometryGeometry

LessonMain

Lesson 9-5

DilationsDilations

9-5

For a dilation with scale factor n, if n > 0, the figure is not turned or flipped. If n < 0, the figure is rotated by 180°.

Helpful Hint

FeatureLesson

GeometryGeometry

LessonMain

Lesson 9-5

DilationsDilations

9-5

If the scale factor of a dilation is negative, the preimage is rotated by 180°. For k > 0, a dilation with a scale factor of –k is equivalent to the composition of a dilation with a scale factor of k that is rotated 180° about the center of dilation.

FeatureLesson

GeometryGeometry

LessonMain

Circle A with 3-cm diameter and center C is a dilation of concentric circle B with 8-cm diameter. Describe the dilation.

The circles are concentric, so the dilation has center C.

Because the diameter of the dilation image is smaller, the dilation is a reduction.

The dilation is a reduction with center C and scale factor .38

Lesson 9-5

DilationsDilations

scale factor: diameter of dilation image

diameter of preimage38

=

Quick Check

Additional Examples

9-5

Finding a Scale Factor

FeatureLesson

GeometryGeometry

LessonMain

The scale factor on a museum’s floor plan is 1 : 200. The length and width on the drawing are 8 in. and 6 in. Find the actual dimensions in feet and inches.

Multiply each dimension on the drawing by 200 to find the actual dimensions. Then write the dimensions in feet and inches.

8 in. X 200 = 1600 in. = 133 ft, 4 in.

6 in. X 200 = 1200 in. = 100 ft

The museum floor measures 133 ft, 4 in. by 100 ft.

Lesson 9-5

DilationsDilations

The floor plan is a reduction of the actual dimensions by a scale factor of . 1 200

Quick Check

Additional Examples

9-5

Real-World Connection

FeatureLesson

GeometryGeometry

LessonMain

ABC has vertices A(–2, –3), B(0, 4), and C(6, –12). What are the coordinates of the image of ABC for a dilation with center (0, 0) and scale factor 0.75?

Lesson 9-5

DilationsDilations

The scale factor is 0.75, so use the rule (x, y) (0.75x, 0.75y).

A' is (0.75(–2), 0.75(–3)).

B' is (0.75(0), 0.75(4)).

C' is (0.75(6), 0.75(–12)).

The vertices of the reduction image of ABC are A' (–1.5, –2.25),B' (0, 3), and C' (4.5, –9).

Quick Check

Additional Examples

9-5

Graphing Dilation Images

FeatureLesson

GeometryGeometry

LessonMain

1. A model is a reduction of a real tractor by the scale factor of 1 : 16. Its dimensions are 1.2 ft by 0.6 ft by 0.625 ft. Find the actual dimensions of the tractor. 19.2 ft by 9.6 ft by 10 ft

For Exercises 2 and 3, XYZ has vertices X(3, 1), Y(2, –4), and Z(–2, 0). 2. Use scalar multiplication to find the image of XYZ for a dilation with

center (0, 0) and scale factor 2.5. X (7.5, 2.5), Y (5, –10), Z (–5, 0)

Lesson 9-5

DilationsDilations

3. Draw and label the preimage and image.

For Exercises 4 and 5, DIL is a dilation image of DAT.

4. Identify the center of dilation.

5. Find the scale factor.

D

4

Lesson Quiz

9-5

FeatureLesson

GeometryGeometry

LessonMain

Determine the scale drawing dimensions of a room using a

scale of in. = 1 ft.

1. kitchen: 12 ft by 16 ft 2. bedroom: 8 ft by 10 ft

3. laundry room: 6 ft by 9 ft 4. bathroom: 5 ft by 7 ft

14

(For help, go to Lesson 7-1.)

Lesson 9-5

DilationsDilations

Check Skills You’ll Need

Check Skills You’ll Need

9-5

FeatureLesson

GeometryGeometry

LessonMain

Solutions

Lesson 9-5

DilationsDilations

1. in. = 1 ft 12 • in. = 12 • 1 3 in. = 12 ft; in. = 1 ft 16 • in. =

16 • 1 ft 4 in. = 16 ft. The dimensions of the scale drawing are 3 in. by

4 in.

14

14

14

14

2. in. = 1 ft 8 • in. = 8 • 1 2 in. = 8 ft; in. = 1 ft 10 • in. =

10 • 1 ft 2.5 in. = 10 ft. The dimensions of the scale drawing are 2 in.

by 2.5 in.

14

14

14

14

3. in. = 1 ft 6 • in. = 6 • 1 1.5 in. = 6 ft; in. = 1 ft 9 • in. =

9 • 1 ft 2.25 in. = 9 ft. The dimensions of the scale drawing are 1.5 in.

by 2.25 in.

14

14

14

14

4. in. = 1 ft 5 • in. = 5 • 1 1.25 in. = 5 ft; in. = 1 ft 7 • in. =

7 • 1 ft 1.75 in. = 9 ft. The dimensions of the scale drawing are 1.25

in. by 1.75 in.

14

14

14

14

Check Skills You’ll Need

9-5