Ch. 7 Learning Goal: Ratios & Proportions Learn to find equivalent ratios to create proportions (7-1) Learn to work with rates and ratios (7-2) Learn to use one or more conversion factors to solve rate problems (7-3) Learn to solve proportions (7-4) Learn to identify and create dilations of plane figures (7-5) Learn to determine whether figures are similar, to use scale factors, and to find missing dimensions similar figures (7-6) Learn to make comparisons between and find dimensions of scale drawings and actual objects (7-7) Learn to make comparisons between and find dimensions of scale models and actual objects (7-8) Learn to make scale models of solid figures (7-9)

Pre-Algebra 7-5 Dilations Pre-Algebra Homework Page 364 #7-12 & #20-24 (Spiral Review)

Pre-Algebra 7-5 Dilations 7-5 Dilations Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Pre-Algebra 7-5 Dilations Warm Up Multiply 2. 12   4. –36  Pre-Algebra 7-5 Dilations –   2.5

Pre-Algebra 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.

Pre-Algebra 7-5 Dilations Today’s Learning Goal Assignment Learn to identify and create dilations of plane figures.

Pre-Algebra 7-5 Dilations Vocabulary dilation scale factor center of dilation

Pre-Algebra 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.

Pre-Algebra 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.

Pre-Algebra 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.

Pre-Algebra 7-5 Dilations A scale factor between 0 and 1 reduces a figure. A scale factor greater than 1 enlarges it. Helpful Hint

Pre-Algebra 7-5 Dilations Tell whether each transformation is a dilation. The transformation is a dilation. The transformation is not a dilation. The figure is distorted. Additional Example 1A & 1B: Identifying Dilations A. B.

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

Pre-Algebra 7-5 Dilations Tell whether each transformation is a dilation. The transformation is a dilation. The transformation is not a dilation. The figure is distorted. Additional Example 1C & 1D: Identifying Dilations C. D.

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

Pre-Algebra 7-5 Dilations 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.

Pre-Algebra 7-5 Dilations Dilate the figure by a scale factor of 1.5 with P as the center of dilation. Additional Example 2: Dilating a Figure Multiply each side by 1.5.

Pre-Algebra 7-5 Dilations Dilate the figure by a scale factor of 0.5 with G as the center of dilation. G FH 2 cm Multiply each side by 0.5. Try This: Example 2 G FH 2 cm F’H’ 1 cm

Pre-Algebra 7-5 Dilations 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(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). ABC A’B’C’

Pre-Algebra 7-5 Dilations Try This: Example 3A Dilate the figure by a scale factor of 2. What are the vertices of the image? B C A

Pre-Algebra 7-5 Dilations Try This: Example 3A Continued 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) ABC A’B’C’ The vertices of the image are A’(4, 4), B’(8, 4), and C’(4, 8).

Pre-Algebra 7-5 Dilations Try This: Example 3A Continued B’ C’ A’ B C A

Pre-Algebra 7-5 Dilations 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? 1313 The vertices of the image are A’(1, 3), B’(3, 2), and C’(2, 1). ABC A’B’C’ A(3, 9) A’(3 , 9  ) A’(1, 3) B(9, 6) B’(9 , 6  ) B’(3, 2) C(6, 3) C’(6 , 3  ) C’(2, 1) Multiply the coordinates by to find the vertices of the image. 1313

Pre-Algebra 7-5 Dilations Try This: Example 3B Dilate the figure by a scale factor of 0.5. What are the vertices of the image? B C A

Pre-Algebra 7-5 Dilations Try This: Example 3B Continued 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) ABC A’B’C’ The vertices of the image are A’(2, 2.5), B’(4, 2.5), and C’(2, 4.5).

Pre-Algebra 7-5 Dilations Try This: Example 3B Continued B C A B’ C’ A’

Pre-Algebra 7-5 Dilations 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) P A B C C’C’ B’B’A’A’ 2. Dilate the figure by a scale factor of 1.5 with P as 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