7-5 Dilations Course 3 Warm Up Problem of the Day Lesson Presentation

7-5 Dilations Warm Up Multiply. 1. 4  2. 12  3. 24  4. –36  3 9 18 Course 3 7-5 Dilations Warm Up Multiply. 1. 4  2. 12  3. 24  4. –36  3 4 3 4 3 9 3 4 3 4 18 –27 5. 4  2.5 6. 12  2.5 10 30

7-5 Dilations Problem of the Day Course 3 7-5 Dilations 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.

7-5 Dilations Learn to identify and create dilations of plane figures. Course 3 7-5 Dilations Learn to identify and create dilations of plane figures.

Insert Lesson Title Here Course 3 7-5 Dilations Insert Lesson Title Here Vocabulary dilation scale factor center of dilation

Course 3 7-5 Dilations Your pupils are the black areas in the center of your eyes. When you go to the eye doctor, the doctor may dilate your pupils, which makes them larger.

Course 3 7-5 Dilations Translations, reflections, and rotations are transformations that do not change the size or shape of a figure. A dilation is a transformation that changes the size, but not the shape, of a figure. A dilation can enlarge or reduce a figure.

Course 3 7-5 Dilations A scale factor describes how much a figure is enlarged or reduced. A scale factor can be expressed as a decimal, fraction, or percent. A 10% increase is a scale factor of 1.1, and a 10% decrease is a scale factor of 0.9.

Insert Lesson Title Here Course 3 7-5 Dilations Insert Lesson Title Here A scale factor between 0 and 1 reduces a figure. A scale factor greater than 1 enlarges it. Helpful Hint

Insert Lesson Title Here Course 3 7-5 Dilations Insert Lesson Title Here Additional Example 1A & 1B: Identifying Dilations Tell whether each transformation is a dilation. A. B. The transformation is not a dilation. The figure is distorted. The transformation is a dilation.

Insert Lesson Title Here Course 3 7-5 Dilations Insert Lesson Title Here Additional Example 1C & 1D: Identifying Dilations Tell whether each transformation is a dilation. D. C. The transformation is not a dilation. The figure is distorted. The transformation is a dilation.

7-5 Dilations Try This: Example 1A & 1B Course 3 7-5 Dilations Try This: Example 1A & 1B Tell whether each transformation is a dilation. B A C A' B' C' A. A B C B. A' B' C' The transformation is a dilation. The transformation is not a dilation. The figure is distorted.

7-5 Dilations Try This: Example 1C & 1D Course 3 7-5 Dilations Try This: Example 1C & 1D Tell whether each transformation is a dilation. D. A' B' C' A B C C. A' B' C' A B C The transformation is not a dilation. The figure is distorted. The transformation is a dilation.

Insert Lesson Title Here Course 3 7-5 Dilations Insert Lesson Title Here Every dilation has a fixed point that is the center 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 the center of dilation.

Insert Lesson Title Here Course 3 7-5 Dilations Insert Lesson Title Here Additional Example 2: Dilating a Figure Dilate the figure by a scale factor of 1.5 with P as the center of dilation. Multiply each side by 1.5.

Insert Lesson Title Here Course 3 7-5 Dilations Insert Lesson Title Here Try This: Example 2 Dilate the figure by a scale factor of 0.5 with G as the center of dilation. G F H 2 cm F’ H’ 1 cm G 2 cm 2 cm F H 2 cm Multiply each side by 0.5.

Additional Example 3A: Using the Origin as the Center of Dilation Course 3 7-5 Dilations Insert Lesson Title Here Additional Example 3A: Using the Origin as the Center of Dilation Dilate the figure in Example 3A on page 363 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. A’B’C’ ABC A(4, 8) A’(4  2, 8  2) A’(8, 16) B(3, 2) B’(3  2, 2  2) B’(6, 4) C(5, 2) C’(5  2, 2  2) C’(10, 4) The vertices of the image are A’(8, 16), B’(6, 4), and C’(10, 4).

Insert Lesson Title Here Course 3 7-5 Dilations Insert Lesson Title Here Additional Example 3B: Using the Origin as the Center of Dilation Dilate the figure in Example 3B by a scale factor of . What are the vertices of the image? 1 3 Multiply the coordinates by to find the vertices of the image. 1 3 A’B’C’ ABC A(3, 9) A’(3  , 9  ) A’(1, 3) 1 3 B(9, 6) B’(9  , 6  ) B’(3, 2) 1 3 C(6, 3) C’(6  , 3  ) C’(2, 1) 1 3 The vertices of the image are A’(1, 3), B’(3, 2), and C’(2, 1).

Insert Lesson Title Here Course 3 7-5 Dilations Insert Lesson Title Here Try This: Example 3A Dilate the figure by a scale factor of 2. What are the vertices of the image? 10 8 6 C 4 2 A B 2 4 6 8 10

Insert Lesson Title Here Course 3 7-5 Dilations Insert Lesson Title Here Try This: Example 3A Continued A’B’C’ ABC A(2, 2) A’(2  2, 2  2) A’(4, 4) B(4, 2) B’(4  2, 2  2) B’(8, 4) C(2, 4) C’(2  2, 4  2) C’(4, 8) The vertices of the image are A’(4, 4), B’(8, 4), and C’(4, 8).

Insert Lesson Title Here Course 3 7-5 Dilations Insert Lesson Title Here Try This: Example 3A Continued 10 B’ C’ A’ 8 6 C 4 2 A B 2 4 6 8 10

Insert Lesson Title Here Course 3 7-5 Dilations Insert Lesson Title Here Try This: Example 3B Dilate the figure by a scale factor of 0.5. What are the vertices of the image? 10 C 8 6 A B 4 2 2 4 6 8 10

Insert Lesson Title Here Course 3 7-5 Dilations Insert Lesson Title Here Try This: Example 3B Continued A’B’C’ ABC A(4, 5) A’(4  0.5, 5  0.5) A’(2, 2.5) B(8, 5) B’(8  0.5, 5  0.5) B’(4, 2.5) C(4, 9) C’(4  0.5, 9  0.5) C’(2, 4.5) The vertices of the image are A’(2, 2.5), B’(4, 2.5), and C’(2, 4.5).

Insert Lesson Title Here Course 3 7-5 Dilations Insert Lesson Title Here Try This: Example 3B Continued 10 C 8 6 B’ C’ A’ A B 4 2 2 4 6 8 10

Insert Lesson Title Here Course 3 7-5 Dilations Insert Lesson Title Here Lesson Quiz 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) yes 2 4 6 2. Dilate the figure by a scale factor of 1.5 with P as the center of dilation. P A B C C’ B’ A’ -2 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) -4 -6 A’(4,8) B’(10,12) C’(12,2)