Unit 5 - Test Study Guide

Transcription

1 Class: Date: Unit 5 - Test Study Guide 1. Which of these transformations appear to be a rigid motion? (I) parallelogram EFGH parallelogram XWVU (II) hexagon CDEFGH hexagon YXWVUT (III) triangle EFG triangle VWU A. I only B. II and III only C. I and II only D. I, II, and III In the diagram, figure RQTS is the image of figure DEFC after a rigid motion. 2. Name the image of F. A. T B. R C. Q D. S 3. Name the image of FC. A. TQ B. ST C. RS D. QR 1

2 4. Which graph shows T < 3,3> ( ABC)? A. C. B. D. 2

3 5. Which graph shows T < 4,2> ( ABC)? A. C. B. D. 3

4 Use the diagram. 6. Find the image of C under the translation described by the translation rule T < 4,5> (C). A. B B. E C. A D. D 7. Find the translation rule that describes the translation B E. A. T < 8,14> (B) C. T < 4,10> (A) B. T < 0,15> (B) D. T < 7,2> (B) 8. The vertices of a rectangle are R( 5, 5), S( 1, 5), T( 1, 1), and U( 5, 1). A translation maps R to the point ( 4, 2). Find the translation rule and the image of U. A. T < 1,7> (RSTU); ( 6, 8) B. T < 1,7> (RSTU); ( 4, 8) C. T < 1, 7> (RSTU); ( 4, 6) D. T < 1, 7> (RSTU); ( 6, 6) 9. Describe in words the translation of X represented by the translation rule T < 2,8> (X). A. 2 units to the left and 8 units up B. 2 units to the right and 8 units down C. 8 units to the left and 2 units down D. 2 units to the right and 8 units up 10. Use a translation rule to describe the translation of X that is 5 units to the left and 7 units up. A. T < 5,7> (X) C. T < 5, 7> (X) B. T < 5,7> (X) D. T < 5, 7> (X) 4

5 11. Jessica was sitting in row 9, seat 3 at a soccer game when she discovered her ticket was for row 1, seat 1. Write a rule to describe the translation needed to put her in the proper seat. A. T <-8,2> (Jessica) C. T <-8,-2> (Jessica) B. T <8,2> (Jessica) D. T <8,-2> (Jessica) 12. Use a translation rule to describe the translation of P that is 6 units to the left and 6 units down. A. T < 6,6> (P) C. T < 6, 6> (P) B. T < 6,6> (P) D. T < 6, 6> (P) 13. What is a rule that describes the translation ABCD A B C D? A. T < 3, 2> (ABCD) C. T < 2, 3> (ABCD) B. T < 3,2> (ABCD) D. T < 3,2> (ABCD) 14. Use a translation rule to describe the translation of ABC that is 8 units to the right and 2 units down. A. T < 8,2> ( ABC) C. T < 8,2> ( ABC) B. T < 8, 2> ( ABC) D. T < 8, 2> ( ABC) 15. What translation rule can be used to describe the result of the composition of T < 5, 3> (x,y) and T < 7, 1> (x,y)? A. T < 12, 4> (x,y) C. T < 4, 12> (x,y) B. T < 12, 4> (x,y) D. T < 2, 2> (x,y) 5

6 16. In the diagram, the dashed-lined figure is the image of the solid-lined figure after a rigid motion. a. List all pairs of corresponding sides. b. Name the image of point C. 17. What are the vertices of T < 2,2> ( ABC)? Graph T < 2,2> ( ABC). 18. Megan left her house and walked 5 blocks north and 4 blocks east to a friend s house. From there, she walked 5 blocks north and 6 blocks west to school for volleyball practice. a. If Megan s house is at the origin, sketch the transformations of her route. b. Describe where the school is in relation to Megan s house in words and using function notation. 19. Write a rule in function notation to describe the transformation that is a reflection across the y-axis. A. R y=x (x,y) C. R y=0 (x,y) B. R x=0 (x,y) D. R x= 1 (x,y) 20. The vertices of a triangle are P( 8, 6), Q(1, 3), and R( 6, 3). Name the vertices of R y=x ( A. P ( 6, 8), Q (3, 1), R (3, 6) C. P ( 6, 8), Q (3, 1), R ( 3,6) B. P (6, 8), Q ( 3, 1), R ( 3, 6) D. P (6, 8), Q ( 3, 1), R ( 3, 6) PQR). 6

7 21. The vertices of a triangle are P( 3, 8), Q( 6, 4), and R(1, 1). Name the vertices of R y=0 ( A. P (3, 8), Q (6, 4), R ( 1, 1) C. P ( 3, 8), Q ( 6, 4), R (1, 1) B. P ( 3, 8), Q ( 6, 4), R (1, 1) D. P (3, 8), Q (6, 4), R ( 1, 1) PQR). 22. The vertices of a triangle are P( 2, 4), Q(2, 5), and R( 1, 8). Name the vertices of R x=0 ( A. P ( 2, 4), Q (2, 5), R ( 1, 8) C. P (2, 4), Q ( 2, 5), R (1, 8) B. P ( 2,4), Q (2,5), R ( 1,8) D. P (2, 4), Q ( 2, 5), R (1, 8) PQR). 23. Write a rule in function notation to describe the transformation that is a reflection across the x-axis. A. R y=x (x,y) C. R x=0 (x,y) B. R x=y (x,y) D. R y=0 (x,y) 24. Find the image of P( 2, 1) after two reflections; first R y= 5 (P), and then R x=1 (P' ). A. ( 2, 1) B. ( 1, 6) C. (4, 9) D. (1, 5) 7

8 25. Which graph shows a triangle and its reflection image over the x-axis? A. C. B. D. 8

9 26. Each triangle in the diagram is a reflection of another triangle across one of the given lines. How can you describe Triangle 3 by using a reflection rule? A. R m (Triangle 2) C. R l (Triangle 1) B. R m (Triangle 1) D. R l (Triangle 2) 27. Each triangle in the diagram is a reflection of another triangle across one of the given lines. How can you describe Triangle 2 by using a reflection rule? I. R l (Triangle 3) II. R m (Triangle 2) III. R m (Triangle 1) A. I only C. II and III only B. I and III only D. I, II, and III 9

10 28. Draw R x-axis ( ABC). 29. Graph points A(1, 5), B(5, 2), and C(1, 2). Graph R y=0 ( ABC). 30. In the figure, A B = R k (AB). a. Find and name two points that line k passes through. b. Explain how you know that line k passes through those two points. c. Graph line k and the point C(3, 2) and show its image as a reflection across line k. 10

11 The hexagon GIKMPR and FJN are regular. The dashed line segments form 30 angles. 31. What is r (240,O) (G)? A. P B. I C. K D. O 32. Find r (120,O) (OL). A. OJ B. OF C. OL D. OH 33. A carnival ride is drawn on a coordinate plane so that the first car is located at the point (30,0). What are the coordinates of the first car after a rotation of 270 about the origin? A. ( 30,0) B. (0, 30) C. (0,30) D. ( 15, 15) 34. a. Graph the quadrilateral WXYZ with vertices W(3, 5), X(1, 3), Y( 1, 5), and Z(1, 7). b. Graph r (90,O) (WXYZ) and state the coordinates of the vertices. 35. Which type of isometry is the equivalent of two reflections across intersecting lines? A. glide reflection C. reflection B. rotation D. none of these 36. The glide reflection R y= x û T < 4,1> maps the point P to (4, 3). Find the coordinates of P. A. ( 2, 0) B. (1, 3) C. (0, 2) D. ( 8, 4) 11

12 37. Find (R m û R l )(D). 38. Find (R n û R m û R l )(P). 12

13 39. Find (R m û R l )(B). 40. a. Graph A B = R y=x (AB). b. Graph A B =(R y=0 û T < 8,0> )(AB). c. Describe a single rigid motion that produces the isometry in part (b). 41. Suppose R m (3, 4)=(1,1) and R n (1,1)=( 5,16). Is m n? Explain. 13

14 42. Find the glide reflection image of the black triangle for the composition (R x=1 û T < 0, 7> ). A. C. B. D. Use the composition (R l ûr ( 90,C ) )( ABC)= DEF, shown below. 43. Which angle has an equal measure to m B? A. m D C. m F B. m A D. m E 14

15 44. Which angle has an equal measure to m C? A. m D C. m F B. m A D. m E 45. Which side has an equal measure to BC? A. DE C. EF B. AB D. DF Use the figures below. 46. Write a sequence of rigid motions that maps RST to DEF. A. (R ST û r (270,P) )( RST)= ( DEF) C. r (180,P) ( RST)=( DEF) B. R y=x ( RST)=( DEF) D. (R y=x û r (180,P) )( RST)= ( DEF) 47. Write a sequence of rigid motions that maps AB to XY. A. R x=0 (AB)=(XY) C. (T < 1,0> û r (90,P) )(AB)= (XY) B. (R y=x û r (90,P) )(AB)= (XY) D. (T < 0, 1> û r (90,P) )(AB)= (XY) 15

16 48. In the diagram, ABC LMN. What is a congruence transformation that maps ABC onto LMN? A. (R y= x )( ABC)= ( LMN) B. (r (90,O) û R y= x )( ABC)= ( LMN) C. (R y=x û T < 0, 2> )( ABC)= ( LMN) D. (R y= x û T < 0,2> )( ABC)= ( LMN) 49. Which figures are congruent? A. B D and A C C. B D and E F B. B D D. B D and E F and A C 16

17 50. The dashed-lined figure is a dilation image of EFGH. Is D (n,h) an enlargement or a reduction? What is the scale factor n of the dilation? A. n = 6; enlargement C. n = 3; reduction B. n = 3; enlargement D. n = 1 3 ; reduction 51. The dashed-lined figure is a dilation image of enlargement, or a reduction? What is the scale factor n of the dilation? ABC with center of dilation P (not shown). Is D (n,p) an A. reduction; n = 2 B. reduction; n = 1 4 C. enlargement; n = 2 D. reduction; n = A blueprint for a house has a scale factor n = 45. A wall in the blueprint is 9 in. What is the length of the actual wall? A. 4,860 feet B in. C. 405 feet D feet 17

18 53. A microscope shows you an image of an object that is 140 times the object s actual size. So the scale factor of the enlargement is 140. An insect has a body length of 6 millimeters. What is the body length of the insect under the microscope? A. 840 centimeters C. 84 millimeters B. 8,400 millimeters D. 840 millimeters 54. The zoom feature on a camera lens allows you dilate what appears on the display. When you change from 100% to 500%, the new image on your screen is an enlargement of the previous image with a scale factor of 5. If the new image is 47.5 millimeters wide, what was the width of the previous image? A. 9.5 millimeters C millimeters B millimeters D millimeters 55. The endpoints of AB are A(9, 4) and B(5, 4). The endpoints of its image after a dilation are A (6, 3) and B (3, 3). a. Explain how to find the scale factor. b. Locate the center of dilation. Show your work. 56. What are the vertices of ABC for D 2 ( ABC)? Graph D 2 ( ABC). 18

19 57. What are the images of the vertices of ABC when you apply the composition D (0.5,O) û R x=4? Graph (D (0.5,O) û R x=4 )( ABC). 58. ABC has vertices A(0,0), B(5, 1), and C(3,7). What are the vertices of the resulting image when the triangle is translated 4 units to the left then dilated by a scale factor of 2? 59. What composition of rigid motions and a dilation maps EFGH to the dashed figure? A. D (3,(2, 2)) û T < 4, 1> C. D (3,(2, 2)) û T < 4,1> B. D ( 1 3,(2, 2)) û T < 4, 1> D. D ( 1 3,(2, 2)) û T < 4,1> 60. You have a 5 by 7 photo that you would like to have enlarged to fit an 8 by 10 frame. Would the two photographs be similar? Explain. 19

20 Unit 5 - Test Study Guide Answer Section 1. ANS: C PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 1 Identifying an Isometry KEY: transformation rigid motion 2. ANS: D PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 2 Naming Images and Corresponding Parts KEY: image preimage rigid motion 3. ANS: B PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 2 Naming Images and Corresponding Parts KEY: image preimage corresponding parts rigid motion 4. ANS: C PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 3 Finding the Image of a Translation KEY: translation transformation image preimage 5. ANS: A PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 3 Finding the Image of a Translation KEY: translation transformation preimage image 6. ANS: B PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 3 Finding the Image of a Translation KEY: translation preimage image 7. ANS: B PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation KEY: translation preimage image 8. ANS: B PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation KEY: translation image preimage 9. ANS: A PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation KEY: translation 10. ANS: B PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation KEY: translation 11. ANS: C PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation KEY: translation word problem 1

21 12. ANS: C PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation KEY: translation 13. ANS: D PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation KEY: translation 14. ANS: D PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation KEY: translation 15. ANS: B PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-1 Problem 5 Composing Translations KEY: translation 16. ANS: a. AB MN, BC NJ, CD JK, DE KL, EA LM b. J PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-1 Problem 2 Naming Images and Corresponding Parts KEY: transformation image preimage multi-part question rigid motion 17. ANS: T < 2,2> (A) = ( 6+2, 2+2) A ( 4, 4) T < 2,2> (B) = ( 2+2, 4+2) B (0, 6) T < 2,2> (C) = ( 4+2, 4+ 2) C ( 2, 2) PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-1 Problem 3 Finding the Image of a Translation KEY: transformation image preimage translation 2

22 18. ANS: a. b. The school is 10 blocks north and 2 block west of Megan s house. School = T < 2,10> (Megan s house) PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 5 Composing Translations KEY: problem solving multi-part question transformation translation word problem 19. ANS: B PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-2 Problem 1 Reflecting a Point Across a Line KEY: reflection line of reflection 20. ANS: B PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-2 Problem 1 Reflecting a Point Across a Line KEY: reflection line of reflection 21. ANS: C PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-2 Problem 1 Reflecting a Point Across a Line KEY: reflection line of reflection 22. ANS: C PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-2 Problem 1 Reflecting a Point Across a Line KEY: reflection line of reflection 23. ANS: D PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-2 Problem 1 Reflecting a Point Across a Line KEY: reflection line of reflection 24. ANS: C PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-2 Problem 1 Reflecting a Point Across a Line KEY: reflection line of reflection 3

23 25. ANS: D PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-2 Problem 2 Graphing a Reflection Image KEY: reflection line of reflection 26. ANS: D PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-2 Problem 3 Writing a Reflection Rule KEY: reflection line of reflection 27. ANS: B PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-2 Problem 3 Writing a Reflection Rule KEY: reflection line of reflection 28. ANS: PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-2 Problem 2 Graphing a Reflection Image KEY: reflection image preimage line of reflection 4

24 29. ANS: PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-2 Problem 2 Graphing a Reflection Image KEY: reflection image preimage line of reflection 30. ANS: [4] a. Answers may vary. Sample: (0, 2) and (2, 0) b. The line that contains the two points is the perpendicular bisector of AA and BB. c. [3] error in calculation of one coordinate of the two points on the line of reflection [2] only two parts correct [1] only one part correct PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-2 Problem 2 Graphing a Reflection Image KEY: reflection reflection line extended response rubric-based question 5

25 31. ANS: C PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-3 Problem 2 Drawing Rotations in a Coordinate Plane KEY: rotation center of rotation angle of rotation 32. ANS: D PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-3 Problem 2 Drawing Rotations in a Coordinate Plane KEY: rotation center of rotation angle of rotation 33. ANS: B PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-3 Problem 2 Drawing Rotations in a Coordinate Plane KEY: rotation center of rotation angle of rotation 34. ANS: a b. Vertices: W (5,3), X (3,1), Y (5, 1), Z (7,1) PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-3 Problem 2 Drawing Rotations in a Coordinate Plane KEY: rotation angle of rotation center of rotation 35. ANS: B PTS: 1 DIF: L2 NAT: CC G.CO.2 CC G.CO.5 CC G.CO.6 G.2.d G.2.g STA: NC 3.01 TOP: 9-4 Problem 2 Reflections Across Intersecting Lines KEY: isometry 36. ANS: A PTS: 1 DIF: L4 NAT: CC G.CO.2 CC G.CO.5 CC G.CO.6 G.2.d G.2.g STA: NC 3.01 TOP: 9-4 Problem 3 Finding a Glide Reflection Image KEY: glide reflection isometry 6

26 37. ANS: PTS: 1 DIF: L3 NAT: CC G.CO.2 CC G.CO.5 CC G.CO.6 G.2.d G.2.g STA: NC 3.01 TOP: 9-4 Problem 1 Composing Reflections Across Parallel Lines KEY: isometry 38. ANS: PTS: 1 DIF: L4 NAT: CC G.CO.2 CC G.CO.5 CC G.CO.6 G.2.d G.2.g STA: NC 3.01 TOP: 9-4 Problem 1 Composing Reflections Across Parallel Lines KEY: isometry 7

27 39. ANS: PTS: 1 DIF: L3 NAT: CC G.CO.2 CC G.CO.5 CC G.CO.6 G.2.d G.2.g STA: NC 3.01 TOP: 9-4 Problem 2 Reflections Across Intersecting Lines KEY: isometry 40. ANS: [4] a-b. c. r (180,O) (AB), a rotation of 180 about the origin [3] description of isometry missing [2] correct coordinates named without graphs [1] only two parts correct PTS: 1 DIF: L4 NAT: CC G.CO.2 CC G.CO.5 CC G.CO.6 G.2.d G.2.g STA: NC 3.01 TOP: 9-4 Problem 3 Finding a Glide Reflection Image KEY: isometry glide reflection extended response rubric-based question rigid motion 8

28 41. ANS: Yes. The reflection lines do not intersect because the three points lie on the same line. Because the line of reflection is the perpendicular bisector of the segment connecting a point and its image, both lines of reflection are perpendicular to the line that passes through all three points. Since both lines of reflection are perpendicular to the same line, they are parallel. PTS: 1 DIF: L4 NAT: CC G.CO.2 CC G.CO.5 CC G.CO.6 G.2.d G.2.g STA: NC 3.01 TOP: 9-4 Problem 1 Reflections Across Parallel Lines KEY: isometry writing in math reasoning 42. ANS: D PTS: 1 DIF: L3 NAT: CC G.CO.2 CC G.CO.5 CC G.CO.6 G.2.d G.2.g STA: NC 3.01 TOP: 9-4 Problem 3 Finding a Glide Reflection Image KEY: isometry glide reflection 43. ANS: C PTS: 1 DIF: L2 NAT: CC G.CO.6 CC G.CO.7 CC G.CO.8 STA: NC 3.01 TOP: 9-5 Problem 1 Identifying Equal Measures 44. ANS: D PTS: 1 DIF: L2 NAT: CC G.CO.6 CC G.CO.7 CC G.CO.8 STA: NC 3.01 TOP: 9-5 Problem 1 Identifying Equal Measures 45. ANS: C PTS: 1 DIF: L2 NAT: CC G.CO.6 CC G.CO.7 CC G.CO.8 STA: NC 3.01 TOP: 9-5 Problem 1 Identifying Equal Measures 46. ANS: A PTS: 1 DIF: L2 NAT: CC G.CO.6 CC G.CO.7 CC G.CO.8 STA: NC 3.01 TOP: 9-5 Problem 2 Identifying Congruent Figures KEY: congruent rigid motion 47. ANS: C PTS: 1 DIF: L2 NAT: CC G.CO.6 CC G.CO.7 CC G.CO.8 STA: NC 3.01 TOP: 9-5 Problem 2 Identifying Congruent Figures KEY: congruent rigid motion 48. ANS: D PTS: 1 DIF: L4 NAT: CC G.CO.6 CC G.CO.7 CC G.CO.8 STA: NC 3.01 TOP: 9-5 Problem 3 Identifying Congruence Transformations KEY: congruent congruence transformation 49. ANS: C PTS: 1 DIF: L2 NAT: CC G.CO.6 CC G.CO.7 CC G.CO.8 STA: NC 3.01 TOP: 9-5 Problem 5 Determining Congruence KEY: congruent congruence transformation 50. ANS: B PTS: 1 DIF: L3 NAT: CC G.CO.2 G.2.c G.2.d STA: NC 3.01 TOP: 9-6 Problem 1 Finding a Scale Factor KEY: dilation enlargement scale factor 51. ANS: D PTS: 1 DIF: L3 NAT: CC G.CO.2 G.2.c G.2.d STA: NC 3.01 TOP: 9-6 Problem 1 Finding a Scale Factor KEY: dilation reduction scale factor 52. ANS: D PTS: 1 DIF: L3 NAT: CC G.CO.2 G.2.c G.2.d STA: NC 3.01 TOP: 9-6 Problem 3 Using a Scale Factor to Find a Length KEY: dilation enlargement scale factor word problem 53. ANS: D PTS: 1 DIF: L3 NAT: CC G.CO.2 G.2.c G.2.d STA: NC 3.01 TOP: 9-6 Problem 3 Using a Scale Factor to Find a Length KEY: dilation enlargement scale factor word problem 9

29 54. ANS: A PTS: 1 DIF: L4 NAT: CC G.CO.2 G.2.c G.2.d STA: NC 3.01 TOP: 9-6 Problem 3 Using a Scale Factor to Find a Length KEY: dilation enlargement scale factor word problem 55. ANS: a. Find the length of each segment. Then divide the length of the image by the length of the preimage. AB= (9 5) 2 + (4 ( 4)) 2 = 4 5 b. A B = (6 3) 2 + (3 ( 3)) 2 = 3 5 The scale factor is , or 3 4. The center is ( 3, 0). PTS: 1 DIF: L4 NAT: CC G.CO.2 G.2.c G.2.d STA: NC 3.01 TOP: 9-6 Problem 1 Finding a Scale Factor KEY: multi-part question dilation reduction center of dilation scale factor coordinate plane graphing 10

30 56. ANS: D 2 (A)=((2) ( 2),(2) (4)), or A ( 4,8) D 2 (B)=((2) (4),(2) (2)), or B (8,4) D 2 (C)=((2) ( 4),(2) ( 4)), or C ( 8, 8) PTS: 1 DIF: L4 NAT: CC G.CO.2 G.2.c G.2.d STA: NC 3.01 TOP: 9-6 Problem 2 Finding a Dilation Image KEY: dilation reduction center of dilation scale factor coordinate plane graphing 57. ANS: A =(5,2) B =(2,1) C =(6, 2) PTS: 1 DIF: L3 NAT: CC G.SRT.2 CC G.SRT.3 STA: NC 3.01 TOP: 9-7 Problem 1 Drawing Transformations 11

31 58. ANS: T < 4,0> (A)=(0 4,0)=A ( 4,0) T < 4,0> (B)=(5 4, 1)=B (1, 1) T < 4,0> (C)=(3 4,7)=C ( 1,7) D 2 (A )=(2 ( 4),2 0)=A ( 8,0) D 2 (B )=(2 1,2 ( 1))=B (2, 2) D 2 (C )=(2 ( 1),2 7)=C ( 2,14) PTS: 1 DIF: L3 NAT: CC G.SRT.2 CC G.SRT.3 STA: NC 3.01 TOP: 9-7 Problem 1 Drawing Transformations 59. ANS: A PTS: 1 DIF: L4 NAT: CC G.SRT.2 CC G.SRT.3 STA: NC 3.01 TOP: 9-7 Problem 2 Describing Transformations KEY: similar similarity transformation rigid motion 60. ANS: No, the two photographs would not be similar. In order for them to be similar, all measurements would have to be multiplied by the same scale factor. PTS: 1 DIF: L2 NAT: CC G.SRT.2 CC G.SRT.3 STA: NC 3.01 TOP: 9-7 Problem 4 Determining Similarity KEY: similarity similarity transformation 12

32 Class: Date: Unit 5 - Test Study Guide 1. Which of these transformations appear to be a rigid motion? (I) parallelogram EFGH parallelogram XWVU (II) hexagon CDEFGH hexagon YXWVUT (III) triangle EFG triangle VWU A. I only B. II and III only C. I and II only D. I, II, and III In the diagram, figure RQTS is the image of figure DEFC after a rigid motion. 2. Name the image of F. A. T B. R C. Q D. S 3. Name the image of FC. A. TQ B. ST C. RS D. QR 1

33 4. Which graph shows T < 3,3> ( ABC)? A. C. B. D. 2

34 5. Which graph shows T < 4,2> ( ABC)? A. C. B. D. 3

35 Use the diagram. 6. Find the image of C under the translation described by the translation rule T < 4,5> (C). A. B B. E C. A D. D 7. Find the translation rule that describes the translation B E. A. T < 8,14> (B) C. T < 4,10> (A) B. T < 0,15> (B) D. T < 7,2> (B) 8. The vertices of a rectangle are R( 5, 5), S( 1, 5), T( 1, 1), and U( 5, 1). A translation maps R to the point ( 4, 2). Find the translation rule and the image of U. A. T < 1,7> (RSTU); ( 6, 8) B. T < 1,7> (RSTU); ( 4, 8) C. T < 1, 7> (RSTU); ( 4, 6) D. T < 1, 7> (RSTU); ( 6, 6) 9. Describe in words the translation of X represented by the translation rule T < 2,8> (X). A. 2 units to the left and 8 units up B. 2 units to the right and 8 units down C. 8 units to the left and 2 units down D. 2 units to the right and 8 units up 10. Use a translation rule to describe the translation of X that is 5 units to the left and 7 units up. A. T < 5,7> (X) C. T < 5, 7> (X) B. T < 5,7> (X) D. T < 5, 7> (X) 4

36 11. Jessica was sitting in row 9, seat 3 at a soccer game when she discovered her ticket was for row 1, seat 1. Write a rule to describe the translation needed to put her in the proper seat. A. T <-8,2> (Jessica) C. T <-8,-2> (Jessica) B. T <8,2> (Jessica) D. T <8,-2> (Jessica) 12. Use a translation rule to describe the translation of P that is 6 units to the left and 6 units down. A. T < 6,6> (P) C. T < 6, 6> (P) B. T < 6,6> (P) D. T < 6, 6> (P) 13. What is a rule that describes the translation ABCD A B C D? A. T < 3, 2> (ABCD) C. T < 2, 3> (ABCD) B. T < 3,2> (ABCD) D. T < 3,2> (ABCD) 14. Use a translation rule to describe the translation of ABC that is 8 units to the right and 2 units down. A. T < 8,2> ( ABC) C. T < 8,2> ( ABC) B. T < 8, 2> ( ABC) D. T < 8, 2> ( ABC) 15. What translation rule can be used to describe the result of the composition of T < 5, 3> (x,y) and T < 7, 1> (x,y)? A. T < 12, 4> (x,y) C. T < 4, 12> (x,y) B. T < 12, 4> (x,y) D. T < 2, 2> (x,y) 5

37 16. In the diagram, the dashed-lined figure is the image of the solid-lined figure after a rigid motion. a. List all pairs of corresponding sides. b. Name the image of point C. 17. What are the vertices of T < 2,2> ( ABC)? Graph T < 2,2> ( ABC). 18. Megan left her house and walked 5 blocks north and 4 blocks east to a friend s house. From there, she walked 5 blocks north and 6 blocks west to school for volleyball practice. a. If Megan s house is at the origin, sketch the transformations of her route. b. Describe where the school is in relation to Megan s house in words and using function notation. 19. Write a rule in function notation to describe the transformation that is a reflection across the y-axis. A. R y=x (x,y) C. R y=0 (x,y) B. R x=0 (x,y) D. R x= 1 (x,y) 20. The vertices of a triangle are P( 8, 6), Q(1, 3), and R( 6, 3). Name the vertices of R y=x ( A. P ( 6, 8), Q (3, 1), R (3, 6) C. P ( 6, 8), Q (3, 1), R ( 3,6) B. P (6, 8), Q ( 3, 1), R ( 3, 6) D. P (6, 8), Q ( 3, 1), R ( 3, 6) PQR). 6

38 21. The vertices of a triangle are P( 3, 8), Q( 6, 4), and R(1, 1). Name the vertices of R y=0 ( A. P (3, 8), Q (6, 4), R ( 1, 1) C. P ( 3, 8), Q ( 6, 4), R (1, 1) B. P ( 3, 8), Q ( 6, 4), R (1, 1) D. P (3, 8), Q (6, 4), R ( 1, 1) PQR). 22. The vertices of a triangle are P( 2, 4), Q(2, 5), and R( 1, 8). Name the vertices of R x=0 ( A. P ( 2, 4), Q (2, 5), R ( 1, 8) C. P (2, 4), Q ( 2, 5), R (1, 8) B. P ( 2,4), Q (2,5), R ( 1,8) D. P (2, 4), Q ( 2, 5), R (1, 8) PQR). 23. Write a rule in function notation to describe the transformation that is a reflection across the x-axis. A. R y=x (x,y) C. R x=0 (x,y) B. R x=y (x,y) D. R y=0 (x,y) 24. Find the image of P( 2, 1) after two reflections; first R y= 5 (P), and then R x=1 (P' ). A. ( 2, 1) B. ( 1, 6) C. (4, 9) D. (1, 5) 7

39 25. Which graph shows a triangle and its reflection image over the x-axis? A. C. B. D. 8

40 26. Each triangle in the diagram is a reflection of another triangle across one of the given lines. How can you describe Triangle 3 by using a reflection rule? A. R m (Triangle 2) C. R l (Triangle 1) B. R m (Triangle 1) D. R l (Triangle 2) 27. Each triangle in the diagram is a reflection of another triangle across one of the given lines. How can you describe Triangle 2 by using a reflection rule? I. R l (Triangle 3) II. R m (Triangle 2) III. R m (Triangle 1) A. I only C. II and III only B. I and III only D. I, II, and III 9

41 28. Draw R x-axis ( ABC). 29. Graph points A(1, 5), B(5, 2), and C(1, 2). Graph R y=0 ( ABC). 30. In the figure, A B = R k (AB). a. Find and name two points that line k passes through. b. Explain how you know that line k passes through those two points. c. Graph line k and the point C(3, 2) and show its image as a reflection across line k. 10

42 The hexagon GIKMPR and FJN are regular. The dashed line segments form 30 angles. 31. What is r (240,O) (G)? A. P B. I C. K D. O 32. Find r (120,O) (OL). A. OJ B. OF C. OL D. OH 33. A carnival ride is drawn on a coordinate plane so that the first car is located at the point (30,0). What are the coordinates of the first car after a rotation of 270 about the origin? A. ( 30,0) B. (0, 30) C. (0,30) D. ( 15, 15) 34. a. Graph the quadrilateral WXYZ with vertices W(3, 5), X(1, 3), Y( 1, 5), and Z(1, 7). b. Graph r (90,O) (WXYZ) and state the coordinates of the vertices. 35. Which type of isometry is the equivalent of two reflections across intersecting lines? A. glide reflection C. reflection B. rotation D. none of these 36. The glide reflection R y= x û T < 4,1> maps the point P to (4, 3). Find the coordinates of P. A. ( 2, 0) B. (1, 3) C. (0, 2) D. ( 8, 4) 11

43 37. Find (R m û R l )(D). 38. Find (R n û R m û R l )(P). 12

44 39. Find (R m û R l )(B). 40. a. Graph A B = R y=x (AB). b. Graph A B =(R y=0 û T < 8,0> )(AB). c. Describe a single rigid motion that produces the isometry in part (b). 41. Suppose R m (3, 4)=(1,1) and R n (1,1)=( 5,16). Is m n? Explain. 13

45 42. Find the glide reflection image of the black triangle for the composition (R x=1 û T < 0, 7> ). A. C. B. D. Use the composition (R l ûr ( 90,C ) )( ABC)= DEF, shown below. 43. Which angle has an equal measure to m B? A. m D C. m F B. m A D. m E 14

46 44. Which angle has an equal measure to m C? A. m D C. m F B. m A D. m E 45. Which side has an equal measure to BC? A. DE C. EF B. AB D. DF Use the figures below. 46. Write a sequence of rigid motions that maps RST to DEF. A. (R ST û r (270,P) )( RST)= ( DEF) C. r (180,P) ( RST)=( DEF) B. R y=x ( RST)=( DEF) D. (R y=x û r (180,P) )( RST)= ( DEF) 47. Write a sequence of rigid motions that maps AB to XY. A. R x=0 (AB)=(XY) C. (T < 1,0> û r (90,P) )(AB)= (XY) B. (R y=x û r (90,P) )(AB)= (XY) D. (T < 0, 1> û r (90,P) )(AB)= (XY) 15

47 48. In the diagram, ABC LMN. What is a congruence transformation that maps ABC onto LMN? A. (R y= x )( ABC)= ( LMN) B. (r (90,O) û R y= x )( ABC)= ( LMN) C. (R y=x û T < 0, 2> )( ABC)= ( LMN) D. (R y= x û T < 0,2> )( ABC)= ( LMN) 49. Which figures are congruent? A. B D and A C C. B D and E F B. B D D. B D and E F and A C 16

48 50. The dashed-lined figure is a dilation image of EFGH. Is D (n,h) an enlargement or a reduction? What is the scale factor n of the dilation? A. n = 6; enlargement C. n = 3; reduction B. n = 3; enlargement D. n = 1 3 ; reduction 51. The dashed-lined figure is a dilation image of enlargement, or a reduction? What is the scale factor n of the dilation? ABC with center of dilation P (not shown). Is D (n,p) an A. reduction; n = 2 B. reduction; n = 1 4 C. enlargement; n = 2 D. reduction; n = A blueprint for a house has a scale factor n = 45. A wall in the blueprint is 9 in. What is the length of the actual wall? A. 4,860 feet B in. C. 405 feet D feet 17

49 53. A microscope shows you an image of an object that is 140 times the object s actual size. So the scale factor of the enlargement is 140. An insect has a body length of 6 millimeters. What is the body length of the insect under the microscope? A. 840 centimeters C. 84 millimeters B. 8,400 millimeters D. 840 millimeters 54. The zoom feature on a camera lens allows you dilate what appears on the display. When you change from 100% to 500%, the new image on your screen is an enlargement of the previous image with a scale factor of 5. If the new image is 47.5 millimeters wide, what was the width of the previous image? A. 9.5 millimeters C millimeters B millimeters D millimeters 55. The endpoints of AB are A(9, 4) and B(5, 4). The endpoints of its image after a dilation are A (6, 3) and B (3, 3). a. Explain how to find the scale factor. b. Locate the center of dilation. Show your work. 56. What are the vertices of ABC for D 2 ( ABC)? Graph D 2 ( ABC). 18

50 57. What are the images of the vertices of ABC when you apply the composition D (0.5,O) û R x=4? Graph (D (0.5,O) û R x=4 )( ABC). 58. ABC has vertices A(0,0), B(5, 1), and C(3,7). What are the vertices of the resulting image when the triangle is translated 4 units to the left then dilated by a scale factor of 2? 59. What composition of rigid motions and a dilation maps EFGH to the dashed figure? A. D (3,(2, 2)) û T < 4, 1> C. D (3,(2, 2)) û T < 4,1> B. D ( 1 3,(2, 2)) û T < 4, 1> D. D ( 1 3,(2, 2)) û T < 4,1> 60. You have a 5 by 7 photo that you would like to have enlarged to fit an 8 by 10 frame. Would the two photographs be similar? Explain. 19

51 Unit 5 - Test Study Guide Answer Section 1. ANS: C PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 1 Identifying an Isometry KEY: transformation rigid motion 2. ANS: D PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 2 Naming Images and Corresponding Parts KEY: image preimage rigid motion 3. ANS: B PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 2 Naming Images and Corresponding Parts KEY: image preimage corresponding parts rigid motion 4. ANS: C PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 3 Finding the Image of a Translation KEY: translation transformation image preimage 5. ANS: A PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 3 Finding the Image of a Translation KEY: translation transformation preimage image 6. ANS: B PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 3 Finding the Image of a Translation KEY: translation preimage image 7. ANS: B PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation KEY: translation preimage image 8. ANS: B PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation KEY: translation image preimage 9. ANS: A PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation KEY: translation 10. ANS: B PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation KEY: translation 11. ANS: C PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation KEY: translation word problem 1

52 12. ANS: C PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation KEY: translation 13. ANS: D PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation KEY: translation 14. ANS: D PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 4 Writing a Rule to Describe a Translation KEY: translation 15. ANS: B PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-1 Problem 5 Composing Translations KEY: translation 16. ANS: a. AB MN, BC NJ, CD JK, DE KL, EA LM b. J PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-1 Problem 2 Naming Images and Corresponding Parts KEY: transformation image preimage multi-part question rigid motion 17. ANS: T < 2,2> (A) = ( 6+2, 2+2) A ( 4, 4) T < 2,2> (B) = ( 2+2, 4+2) B (0, 6) T < 2,2> (C) = ( 4+2, 4+ 2) C ( 2, 2) PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-1 Problem 3 Finding the Image of a Translation KEY: transformation image preimage translation 2

53 18. ANS: a. b. The school is 10 blocks north and 2 block west of Megan s house. School = T < 2,10> (Megan s house) PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-1 Problem 5 Composing Translations KEY: problem solving multi-part question transformation translation word problem 19. ANS: B PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-2 Problem 1 Reflecting a Point Across a Line KEY: reflection line of reflection 20. ANS: B PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-2 Problem 1 Reflecting a Point Across a Line KEY: reflection line of reflection 21. ANS: C PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-2 Problem 1 Reflecting a Point Across a Line KEY: reflection line of reflection 22. ANS: C PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-2 Problem 1 Reflecting a Point Across a Line KEY: reflection line of reflection 23. ANS: D PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-2 Problem 1 Reflecting a Point Across a Line KEY: reflection line of reflection 24. ANS: C PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-2 Problem 1 Reflecting a Point Across a Line KEY: reflection line of reflection 3

54 25. ANS: D PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-2 Problem 2 Graphing a Reflection Image KEY: reflection line of reflection 26. ANS: D PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-2 Problem 3 Writing a Reflection Rule KEY: reflection line of reflection 27. ANS: B PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-2 Problem 3 Writing a Reflection Rule KEY: reflection line of reflection 28. ANS: PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-2 Problem 2 Graphing a Reflection Image KEY: reflection image preimage line of reflection 4

55 29. ANS: PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-2 Problem 2 Graphing a Reflection Image KEY: reflection image preimage line of reflection 30. ANS: [4] a. Answers may vary. Sample: (0, 2) and (2, 0) b. The line that contains the two points is the perpendicular bisector of AA and BB. c. [3] error in calculation of one coordinate of the two points on the line of reflection [2] only two parts correct [1] only one part correct PTS: 1 DIF: L4 STA: NC 3.01 TOP: 9-2 Problem 2 Graphing a Reflection Image KEY: reflection reflection line extended response rubric-based question 5

56 31. ANS: C PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-3 Problem 2 Drawing Rotations in a Coordinate Plane KEY: rotation center of rotation angle of rotation 32. ANS: D PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-3 Problem 2 Drawing Rotations in a Coordinate Plane KEY: rotation center of rotation angle of rotation 33. ANS: B PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-3 Problem 2 Drawing Rotations in a Coordinate Plane KEY: rotation center of rotation angle of rotation 34. ANS: a b. Vertices: W (5,3), X (3,1), Y (5, 1), Z (7,1) PTS: 1 DIF: L3 STA: NC 3.01 TOP: 9-3 Problem 2 Drawing Rotations in a Coordinate Plane KEY: rotation angle of rotation center of rotation 35. ANS: B PTS: 1 DIF: L2 NAT: CC G.CO.2 CC G.CO.5 CC G.CO.6 G.2.d G.2.g STA: NC 3.01 TOP: 9-4 Problem 2 Reflections Across Intersecting Lines KEY: isometry 36. ANS: A PTS: 1 DIF: L4 NAT: CC G.CO.2 CC G.CO.5 CC G.CO.6 G.2.d G.2.g STA: NC 3.01 TOP: 9-4 Problem 3 Finding a Glide Reflection Image KEY: glide reflection isometry 6

57 37. ANS: PTS: 1 DIF: L3 NAT: CC G.CO.2 CC G.CO.5 CC G.CO.6 G.2.d G.2.g STA: NC 3.01 TOP: 9-4 Problem 1 Composing Reflections Across Parallel Lines KEY: isometry 38. ANS: PTS: 1 DIF: L4 NAT: CC G.CO.2 CC G.CO.5 CC G.CO.6 G.2.d G.2.g STA: NC 3.01 TOP: 9-4 Problem 1 Composing Reflections Across Parallel Lines KEY: isometry 7

58 39. ANS: PTS: 1 DIF: L3 NAT: CC G.CO.2 CC G.CO.5 CC G.CO.6 G.2.d G.2.g STA: NC 3.01 TOP: 9-4 Problem 2 Reflections Across Intersecting Lines KEY: isometry 40. ANS: [4] a-b. c. r (180,O) (AB), a rotation of 180 about the origin [3] description of isometry missing [2] correct coordinates named without graphs [1] only two parts correct PTS: 1 DIF: L4 NAT: CC G.CO.2 CC G.CO.5 CC G.CO.6 G.2.d G.2.g STA: NC 3.01 TOP: 9-4 Problem 3 Finding a Glide Reflection Image KEY: isometry glide reflection extended response rubric-based question rigid motion 8

59 41. ANS: Yes. The reflection lines do not intersect because the three points lie on the same line. Because the line of reflection is the perpendicular bisector of the segment connecting a point and its image, both lines of reflection are perpendicular to the line that passes through all three points. Since both lines of reflection are perpendicular to the same line, they are parallel. PTS: 1 DIF: L4 NAT: CC G.CO.2 CC G.CO.5 CC G.CO.6 G.2.d G.2.g STA: NC 3.01 TOP: 9-4 Problem 1 Reflections Across Parallel Lines KEY: isometry writing in math reasoning 42. ANS: D PTS: 1 DIF: L3 NAT: CC G.CO.2 CC G.CO.5 CC G.CO.6 G.2.d G.2.g STA: NC 3.01 TOP: 9-4 Problem 3 Finding a Glide Reflection Image KEY: isometry glide reflection 43. ANS: C PTS: 1 DIF: L2 NAT: CC G.CO.6 CC G.CO.7 CC G.CO.8 STA: NC 3.01 TOP: 9-5 Problem 1 Identifying Equal Measures 44. ANS: D PTS: 1 DIF: L2 NAT: CC G.CO.6 CC G.CO.7 CC G.CO.8 STA: NC 3.01 TOP: 9-5 Problem 1 Identifying Equal Measures 45. ANS: C PTS: 1 DIF: L2 NAT: CC G.CO.6 CC G.CO.7 CC G.CO.8 STA: NC 3.01 TOP: 9-5 Problem 1 Identifying Equal Measures 46. ANS: A PTS: 1 DIF: L2 NAT: CC G.CO.6 CC G.CO.7 CC G.CO.8 STA: NC 3.01 TOP: 9-5 Problem 2 Identifying Congruent Figures KEY: congruent rigid motion 47. ANS: C PTS: 1 DIF: L2 NAT: CC G.CO.6 CC G.CO.7 CC G.CO.8 STA: NC 3.01 TOP: 9-5 Problem 2 Identifying Congruent Figures KEY: congruent rigid motion 48. ANS: D PTS: 1 DIF: L4 NAT: CC G.CO.6 CC G.CO.7 CC G.CO.8 STA: NC 3.01 TOP: 9-5 Problem 3 Identifying Congruence Transformations KEY: congruent congruence transformation 49. ANS: C PTS: 1 DIF: L2 NAT: CC G.CO.6 CC G.CO.7 CC G.CO.8 STA: NC 3.01 TOP: 9-5 Problem 5 Determining Congruence KEY: congruent congruence transformation 50. ANS: B PTS: 1 DIF: L3 NAT: CC G.CO.2 G.2.c G.2.d STA: NC 3.01 TOP: 9-6 Problem 1 Finding a Scale Factor KEY: dilation enlargement scale factor 51. ANS: D PTS: 1 DIF: L3 NAT: CC G.CO.2 G.2.c G.2.d STA: NC 3.01 TOP: 9-6 Problem 1 Finding a Scale Factor KEY: dilation reduction scale factor 52. ANS: D PTS: 1 DIF: L3 NAT: CC G.CO.2 G.2.c G.2.d STA: NC 3.01 TOP: 9-6 Problem 3 Using a Scale Factor to Find a Length KEY: dilation enlargement scale factor word problem 53. ANS: D PTS: 1 DIF: L3 NAT: CC G.CO.2 G.2.c G.2.d STA: NC 3.01 TOP: 9-6 Problem 3 Using a Scale Factor to Find a Length KEY: dilation enlargement scale factor word problem 9

60 54. ANS: A PTS: 1 DIF: L4 NAT: CC G.CO.2 G.2.c G.2.d STA: NC 3.01 TOP: 9-6 Problem 3 Using a Scale Factor to Find a Length KEY: dilation enlargement scale factor word problem 55. ANS: a. Find the length of each segment. Then divide the length of the image by the length of the preimage. AB= (9 5) 2 + (4 ( 4)) 2 = 4 5 b. A B = (6 3) 2 + (3 ( 3)) 2 = 3 5 The scale factor is , or 3 4. The center is ( 3, 0). PTS: 1 DIF: L4 NAT: CC G.CO.2 G.2.c G.2.d STA: NC 3.01 TOP: 9-6 Problem 1 Finding a Scale Factor KEY: multi-part question dilation reduction center of dilation scale factor coordinate plane graphing 10

61 56. ANS: D 2 (A)=((2) ( 2),(2) (4)), or A ( 4,8) D 2 (B)=((2) (4),(2) (2)), or B (8,4) D 2 (C)=((2) ( 4),(2) ( 4)), or C ( 8, 8) PTS: 1 DIF: L4 NAT: CC G.CO.2 G.2.c G.2.d STA: NC 3.01 TOP: 9-6 Problem 2 Finding a Dilation Image KEY: dilation reduction center of dilation scale factor coordinate plane graphing 57. ANS: A =(5,2) B =(2,1) C =(6, 2) PTS: 1 DIF: L3 NAT: CC G.SRT.2 CC G.SRT.3 STA: NC 3.01 TOP: 9-7 Problem 1 Drawing Transformations 11

62 58. ANS: T < 4,0> (A)=(0 4,0)=A ( 4,0) T < 4,0> (B)=(5 4, 1)=B (1, 1) T < 4,0> (C)=(3 4,7)=C ( 1,7) D 2 (A )=(2 ( 4),2 0)=A ( 8,0) D 2 (B )=(2 1,2 ( 1))=B (2, 2) D 2 (C )=(2 ( 1),2 7)=C ( 2,14) PTS: 1 DIF: L3 NAT: CC G.SRT.2 CC G.SRT.3 STA: NC 3.01 TOP: 9-7 Problem 1 Drawing Transformations 59. ANS: A PTS: 1 DIF: L4 NAT: CC G.SRT.2 CC G.SRT.3 STA: NC 3.01 TOP: 9-7 Problem 2 Describing Transformations KEY: similar similarity transformation rigid motion 60. ANS: No, the two photographs would not be similar. In order for them to be similar, all measurements would have to be multiplied by the same scale factor. PTS: 1 DIF: L2 NAT: CC G.SRT.2 CC G.SRT.3 STA: NC 3.01 TOP: 9-7 Problem 4 Determining Similarity KEY: similarity similarity transformation 12