**8**21 4 15 4. 3. 48 42 16 14 ? = n 12 45 18 = Quiz Tell whether this pair of ratios is proportional. 1. Solve the proportion. 2. Find two ratios that are equivalent to each given ratio. Simplify to tell whether the ratios form a proportion. 16 10 32 20 5. and**Dilations**7.5 Pre-Algebra**3 4**3 4 3 4 3 4 Warm Up Multiply. 1. 4 2. 12 3. 24 4. –36 9 3 18 –27 10 30 5. 4 2.5 6. 12 2.5**Vocabulary**dilation scale factor center of dilation**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.**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.**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.**Helpful Hint**A scale factor between 0 and 1 reduces a figure. A scale factor greater than 1 enlarges it.**Example: 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.**Example: Identifying Dilations**Tell whether each transformation is a dilation. C. D. The transformation is not a dilation. The figure is distorted. The transformation is a dilation.**A'**A A' B' B B' C C' C' A B C Try This Tell whether each transformation is a dilation. A. B. The transformation is not a dilation. The figure is distorted. The transformation is a dilation.**A**A A' A' B C C' B' B C C' B' Try This Tell whether each transformation is a dilation. D. C. The transformation is not a dilation. The figure is distorted. The transformation is a dilation.**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.**Example: 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.**G**1 cm 1 cm 2 cm 2 cm F’ H’ 1 cm F H 2 cm Try This Dilate the figure by a scale factor of 0.5 with G as the center of dilation. G 2 cm 2 cm F H 2 cm Multiply each side by 0.5.**A’B’C’**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) ABC Example: 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. The vertices of the image are A’(8, 16), B’(6, 4), and C’(10, 4).**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. A’B’C’ C(6, 3) C’(6 , 3 ) C’(2, 1) B(9, 6) B’(9 , 6 ) B’(3, 2) A(3, 9) A’(3 , 9 ) A’(1, 3) ABC 1 3 1 3 1 3 1 3 1 3 1 3 1 3 Example: Using the Origin as the Center of Dilation The vertices of the image are A’(1, 3), B’(3, 2), and C’(2, 1).**Try This**Dilate the figure by a scale factor of 2. What are the vertices of the image? 10 8 6 C 4 2 A B 10 8 4 6 2 0**A’B’C’**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 Try This The vertices of the image are A’(4, 4), B’(8, 4), and C’(4, 8).**C’**B’ A’ Try This 10 8 6 C 4 2 B A 10 8 4 6 2 0**Try This**Dilate the figure by a scale factor of 0.5. What are the vertices of the image? 10 C 8 6 B A 4 2 10 8 4 6 2 0**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) A’B’C’ ABC C(4, 9) C’(4 0.5, 9 0.5) C’(2, 4.5) Try This The vertices of the image are A’(2, 2.5), B’(4, 2.5), and C’(2, 4.5).**C’**B’ A’ Try This 10 C 8 6 B A 4 2 10 8 4 6 2 0**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 C’ C A B B’ A’ Lesson Quiz yes 2 4 6 2. Dilate the figure by a scale factor of 1.5 with P as the center of dilation. -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)