Dilations. Dilations. Enlarges or Reduces a figure using a scale factor. Name: Period: Date: Dilations. Scale Factor =

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1 Name: Period: Date: Dilations Dilations Enlarges or Reduces a figure using a scale factor. Dilations B B B C 6 C Scale Factor = B C BC has been enlarged by a scale factor of 3. What are the coordinates of its image? (1,1) (, ) C B (1,3) B (, ) C (3,1) C (, ) 1. What is the relationship between the new coordinates and the scale factor? dilation with a scale factor greater than 1 is called an. The image is than the original. 2. If BC is dilated by a scale factor of 4, what are the coordinates of B C? 3. If BC is dilated by a scale factor of 1/3, what are the coordinates of B C? dilation with a scale factor less than 1 is called a. The image is than the original.

2 Practice: 1. rectangle is dilated with a scale factor of 0.6. Is the image a reduction or an enlargement? 2. B B a. Figure has been dilated to figure. What is its scale factor? b. Figure B has been dilated to figure B. What is its scale factor? 3. Find the coordinates of the image of quadrilateral KLMN after a dilation with a scale factor of 3/2. K(, ) _K L M L(, ) _L K N M(, ) _M N(, ) _N 4. You are reducing a digital photo that is 2 in. high and 3 in. wide. If the reduced photo is in. high, what is its width? 5. Find the coordinates of the image of quadrilateral RSTU after a dilation with the given scale factor. Graph the image. a. scale factor: 2 b. scale factor R(, ) S(, ) S R T U T(, ) U(, )

3 WHT EFFECT DOES SCLE FCTOR HVE ON PERIMETER? 6. B C is the image of BC after a dilation. B B 7 cm 24 cm 28 cm C 10 cm SCLE FCTOR and ITS EFFECT ON PERIMETER and RE. C What is the ratio of the perimeter of B C to the perimeter of BC? 2 S 3 T Scale Factor Perimeter of Original Figure 1 10 Perimeter of the Dilation RSTU (2 by 3) R U SF SF 2 rea of Original Figure rea of the Dilation RSTU (2 by 3) 2 10 R S T U (4 by 6) R S T U (4 by 6) 3 10 R S T U (6 by 9) R S T U (6 by 9) 4 10 R S T U (8 by 12) R S T U (8 by 12) What is the result when the original perimeter is multiplied by the scale factor used to dilate the figure? What is the result if the original area is multiplied by the scale factor squared? 7. List the dimensions, the area, and perimeter of rectangle HIJK? Dimensions: rea: Perimeter: 8. Dilate the image by 0.5. Dimensions: rea: Perimeter: I H J K 9. Write the ratio of the dilated perimeter to the original perimeter. Do the same for the areas. 10. Multiply the original perimeter by the scale factor. 11. Multiply the original area by (scale factor) 2.

4 Name: Period: Date: Mixed Practice Homework Translations, Reflections, Rotations, Dilations, Similar Figures, Scale Factor 1. Determine if the following polygons are similar. a. 4. Graph the polygon with the given vertices. Dilate by the scale factor K and graph the image. L( 2, 2), M( 2, 6), N( 6, 10), Q( 6,0); k = b. 2. BC is similar to EFG. Find the value of x. Then find the scale factor if BC is dilated to form EFG? 5. You are making a large gingerbread house that is similar in shape to a real house. The real house is 25 feet tall and 40 feet wide. The gingerbread house is 2.5 feet tall. How wide should you make the gingerbread house? 3. Quadrilateral WXYZ is similar to quadrilateral LMNP. Find the values of x and y. 6. Use the graph to tell what type of transformation is shown.. translation B. reflection over the x-axis C. reflection over the y-axis D. 90 clockwise rotation

5 Use the graph below for questions 7 and If trapezoid BCD is reflected across the y-axis, what will be the new coordinates of the vertices? Graph the image. = B = C = 7. Circle N passes through points (1,1), (5,5), (9,1), and (5,-3). If you slide the circle 2 units up and 2 units to the left, what will be the new coordinates of the center of circle N? D = (5,3) B (4,2) C (3,3) 11. Cheryl drew triangle KLM as shown on the graph below. D (3,2) 8. If you slide triangle DEF 2 units down and 1 unit to the right, what will be the new coordinates of vertex F? (1,1) B (1,5) C (2,1) D (2,2) 9. Margie wants to slide the triangle so that the coordinates for vertex P are (6,1). Write a rule that tells how Margie should slide the triangle. She began to draw a translation of triangle KLM as shown on the graph below. What should the coordinates for vertex K be?

6 12. If triangle RST is reflected across the y-axis, what will be the new coordinates of its image? 14. Describe the transformation below. R = S = T = 15. EFGH is the image of BCD after dilation. The vertices of BCD and EFGH are listed below 13. Which of the following appears to be a reflection over? (-1,2) E(-4,8) B (3,2) F(12,8) Graph the figures below. C (3,-1) G(12,-4) D(-1,-1) H (-4,-4) a. What is the scale factor? b. What is the perimeter of BCD? c. How is the ratio of the perimeter of EFGH to the perimeter of BCD related to the scale factor? d. What is the area of BCD? e. How is the ratio of the area of EFGH to the area of BCD related to the scale factor?

7 16. The vertices of triangle JLK are listed below. J(-4,-3) K(-2,0) 18. Graph LMN with vertices L(2,0), M(2,3), and N(6,0). Then graph its image after the following transformations. a. Rotate 90 counterclockwise. L(1,2) Kim rotated the triangle 90 clockwise. Describe and correct the error Kim made when finding the coordinates of the vertices of the rotated image. b. Reflect over the y-axis. Kim s Work (x,y) (-y,x) J(-4,-3) J (3,-4) K(-2,0) L(1,2) K (0,-2) L (-2,1) The vertices are: (3,-4), (0,-2), and (-2,1) 17. Graph LMN with vertices L(2,0), M(2,3), and N(6,0). Then graph its image after the following transformations. a. Rotate 180. b. Translate using (x, y) (x 3, y 4)