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- 1. Warm Up Problem of the Day Lesson Presentation 5-6 Dilations Course 3

2. Warm Up Multiply. 1.4 2.12 3.24 4.36 3 18 10 9 27 30 5.4 2.5 6.12 2.5 Course 3 5-6 Dilations 3 4 3 4 3 4 3 4 3. Problem of the Day Every day, a plant grows to three times its size. Every night, it shrinks to half its size. After three days and nights, it is 6.75 in. tall. How tall was the plant at the start?2 in. 4. Learnto identify and create dilations of plane figures. 5. Vocabulary dilation center of dilation 6. Your pupils are the black areas in the center of your eyes. When you go to the eye doctor, the doctor maydilateyour pupils, which makes them larger. Translations, reflections, and rotations are transformations that do not change the size or shape of a figure. Adilationis a transformation that changes the size, but not the shape, of a figure. A dilation can enlarge or reduce a figure. 7. Every dilation has a fixed point that is thecenter of dilation . To find the center of dilation, draw a line that connects each pair of corresponding vertices. The lines intersect at one point. This point is thecenter of dilation . 8. Tell whether each transformation is a dilation. The transformationis a dilation. The transformationis not a dilation.The figure is distorted. Additional Example 1: Identifying Dilations A. B. 9. Tell whether each transformation is a dilation. The transformationis a dilation. The transformationis not a dilation.The figure is distorted. Additional Example 1: Identifying Dilations C. D. 10. Tell whether each transformation is a dilation. A. The transformationis a dilation. The transformationis not a dilation.The figure is distorted. Check It Out: Example 1 B. A ' B ' C ' A B C B A C A ' B ' C ' 11. Tell whether each transformation is a dilation. C. The transformationis a dilation. The transformationis not a dilation.The figure is distorted. Check It Out: Example 1 D. A ' B ' C ' A B C A ' B ' C ' A B C 12. Dilate the figure by a scale factor of 1.5 withPas the center of dilation. Additional Example 2: Dilating a Figure Multiply each side by 1.5. 13. Dilate the figure by a scale factor of 0.5 withGas the center of dilation. G F H 2 cm 2 cm 2 cm Multiply each side by 0.5. Check It Out: Example 2 G F H 2 cm 2 cm 2 cm F H 1 cm 1 cm 1 cm 14. Insert Lesson Title Here Course 3 5-6 Dilations A scale factor between 0 and 1 reduces a figure. A scale factor greater than 1 enlarges it. Helpful Hint 15. Additional Example 3A: Using the Origin as the Center of Dilation Dilate the figure below by a scale factor of 2. What are the vertices of the image? Multiply the coordinates by 2 to find the vertices of the image. The vertices of the image areA (8, 16),B (6, 4), andC (10, 4). A (4, 8)A (42 , 82 )A (8, 16) B (3, 2)B (32 , 22 )B (6, 4) C (5, 2)C (52 , 22 )C (10, 4) ABC ABC 16. Additional Example 3B: Using the Origin as the Center of Dilation Dilate the figure below by a scale factor of. What are the vertices of the image? The vertices of the image areA (1, 3),B (3, 2), andC (2, 1). 1 3 ABC ABC A (3, 9)A (3 , 9 )A (1, 3) 13 13 B (9, 6)B (9 , 6 )B (3, 2) 13 13 C (6, 3)C (6 , 3 )C (2, 1) 13 13 Multiply the coordinates byto find the vertices of the image. 13 17. Check It Out: Example 3A Dilate the figure by a scale factor of 2.What are the vertices of the image? 2 4 2 4 6 8 10 0 6 8 10 B C A 18. Check It Out: Example 3A Continued The vertices of the image are A(4, 4), B(8, 4), and C(4, 8). A (2, 2)A (22 , 22 )A (4, 4) B (4, 2)B (42 , 22 )B (8, 4) C (2, 4)C (22 , 42 )C (4, 8) ABC ABC 19. Check It Out: Example 3A Continued 2 4 2 4 6 8 10 0 6 8 10 B C A B C A 20. Check It Out: Example 3B Dilate the figure by a scale factor of 0.5.What are the vertices of the image? 2 4 2 4 6 8 10 0 6 8 10 B C A 21. Check It Out: Example 3B Continued The vertices of the image are A(2, 2.5), B(4, 2.5), and C(2, 4.5). A (4, 5)A (40.5 , 50.5 )A (2, 2.5) B (8, 5)B (80.5 , 50.5 )B (4, 2.5) C (4, 9)C (40.5 , 90.5 )C (2, 4.5) ABC ABC 22. Check It Out: Example 3B Continued 2 4 2 4 6 8 10 0 6 8 10 B C A B C A 23. Lesson Quiz 2 4 6 -2 -4 -6 2.Dilate the figure by a scale factor of 1.5 withPas the center of dilation. 3.Dilate the figure by a scale factor of 2 with the origin as the center of dilation. What are the coordinates of the image?A (2,4)B (5,6)C (6,1)A (4,8)B (10,12)C (12,2) yes 1.Tell whether the transformation is a dilation.A(0, 4) B(5,5) C(3,3)A(0, 8) B(10, 10) C(6, 6) P A B C C B A