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Symmetry

72° rotational symmetry. Symmetry. 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.

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Symmetry

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  1. 72° rotational symmetry Symmetry 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. 9-5

  2. 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. 9-5

  3. Dilations Lesson 9-5 9-5

  4. Dilations Lesson 9-5 9-5

  5. Dilations Helpful Hint 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°. Lesson 9-5 9-5

  6. 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. 9-5

  7. diameter of dilation image diameter of preimage 3 8 scale factor: = 3 8 The dilation is a reduction with center C and scale factor . 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. Quick Check 9-5

  8. 1 200 The floor plan is a reduction of the actual dimensions by a scale factor of . 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. 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 9-5

  9. The vertices of the reduction image of ABC are A' (–1.5, –2.25), B' (0, 3), and C' (4.5, –9). 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)). Quick Check 9-5

  10. For Exercises 2 and 3, XYZ has vertices X(3, 1), Y(2, –4), and Z(–2, 0). For Exercises 4 and 5, DIL is a dilation image of DAT. 2. Use scalar multiplication to find the image of XYZ for a dilation with center (0, 0) and scale factor 2.5. 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 0.625 ft. Find the actual dimensions of the tractor. 19.2 ft by 9.6 ft by 10 ft X (7.5, 2.5), Y (5, –10), Z (–5, 0) 3. Draw and label the preimage and image. 4. Identify the center of dilation. 5. Find the scale factor. D 4 9-5

  11. 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 Dilations Lesson 9-5 Check Skills You’ll Need (For help, go to Lesson 7-1.) Check Skills You’ll Need 9-5

  12. 1 4 1 4 1 4 1 4 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. 1 4 1 4 1 4 1 4 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. 1 4 1 4 1 4 1 4 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. 1 4 1 4 1 4 1 4 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. Dilations Lesson 9-5 Check Skills You’ll Need Solutions 9-5

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