1. Tell what type(s) of symmetry each figure has.
Lesson 9-4
Lesson Quiz
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
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
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4. Dilations
Lesson 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.
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5. Dilations
Lesson 9-5
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6. Dilations
Lesson 9-5
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7. Dilations
Lesson 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
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8. Dilations
Lesson 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.
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9. diameter of dilation image
Dilations
Lesson 9-5
Additional Examples
Finding a Scale Factor
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.
scale factor:
diameter of dilation image
diameter of preimage 3 8 =
The dilation is a reduction with center C and scale factor . 3 8
Quick Check
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10. Real-World Connection
Dilations
Lesson 9-5
Additional Examples
Real-World Connection
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.
The floor plan is a reduction of the actual dimensions by a scale factor of 1
200
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.
Quick Check
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11. Graphing Dilation Images
Dilations
Lesson 9-5
Additional Examples
Graphing Dilation Images
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?
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
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12. 3. Draw and label the preimage and image.
Dilations
Lesson 9-5
Lesson Quiz
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 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)
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
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13. Determine the scale drawing dimensions of a room using a
Dilations
Lesson 9-5
Check Skills You’ll Need
(For help, go to Lesson 7-1.)
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 1 4
Check Skills You’ll Need
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14. Dilations
Lesson 9-5
Check Skills You’ll Need
Solutions
in. = 1 ft • in. = 12 • in. = 12 ft; in. = 1 ft • in. = 16 • 1 ft in. = 16 ft. The dimensions of the scale drawing are 3 in. by 4 in. 1 4
in. = 1 ft • in. = 8 • in. = 8 ft; in. = 1 ft • in. = 10 • 1 ft in. = 10 ft. The dimensions of the scale drawing are 2 in. by 2.5 in.
in. = 1 ft • in. = 6 • in. = 6 ft; in. = 1 ft • in. = 9 • 1 ft in. = 9 ft. The dimensions of the scale drawing are 1.5 in. by 2.25 in.
in. = 1 ft • in. = 5 • in. = 5 ft; in. = 1 ft • in. = 7 • 1 ft in. = 9 ft. The dimensions of the scale drawing are 1.25 in. by 1.75 in.
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