1.9 km north 3 km 4 km

Transcription

1 nswers for Lesson 9-1, pp Eercises 1. Yes; the trans. is a slide.. Yes; the trans. is a flip.. No; the figures are not.. a. nswers ma var. Sample: Q S Q b. QR and QrRr; RS and RrSr; S and Srr; Q and 5. a. nswers ma var. Sample: R S R Qrr b. RI and RrIr; IT and IrTr; RT and RrTr 6. a. nswers ma var. Sample: G S M b. GW and MR; W and RT; N and TX; N and XS; G and SM 7. ( 6, 5), (, 1), (, ) 8. (1, ), (, 1), (10, ), (7, 5) 9. ( 7, 5), ( 7, 8), (, 8), ( 1, ) 10. (, 0.5), (, ), ( 1, ), (5, 0) 11. (, ) S ( 1, ) 1. (, ) S ( 1, 1) 1. (, ) S ( 5, ) 1. (, ) S (, ) 15. a. N b. about 7.1 km west, R 5 km 1.9 km north km km S W E S Geometr Chapter 9 191

2 nswers for Lesson 9-1, pp Eercises (cont.) 16. N Norman is mi east and 81 mi 107 W E south of Enid. Enid 18 8 Tulsa 6 S Norman 17. (, ) S (, ) 18. (, ) S (, 1) 19. D C 10 C E E L I L 10 I 8 E N E 8 N L L T T 1 1. a. t least 5 ft east, 10 ft north b. Sample: (, ) S ( 5, 10). Check students work. 5. U (1, 16), G (, 1) Geometr Chapter 9 19

3 nswers for Lesson 9-1, pp Eercises (cont.) 6. a., b. D C D C 7. No; HY S Y H is the translation 8. (, ) S (, 1) 9. (, ) S ( 1,.5) 0. a. slant involves one translation straight downfield and then another diagonall towards the middle of the field; the composition is one translation. b. The ball drops straight back with the Q and is then thrown to the receiver downfield; the composition is one translation. c. a completion 1.. Geometr Chapter 9 19

4 nswers for Lesson 9-1, pp Eercises (cont.).. Check students work. 5. a. (, 7), (0, 1), C (6, 1) b. midpoint of (, ); midpoint of C ( 1, ); midpoint of C (0, 1); midpoint of 99 (1, ); midpoint of 9C9 (, 0); midpoint of 9C9 (, ); image of (, ) (1, ) midpoint of 99; image of ( 1, ) (, 0) midpoint 9C9; image of (0, 1) (, ) midpoint of 9C9 6. Translate a line segment in a direction different than along the segment. Then connect the endpoints of the line segment and its image to form a ~. Geometr Chapter 9 19

5 nswers for Lesson 9-, pp Eercises 1. ( 1, ). ( 1, ). (, ). (, ) 5. ( 5, ) J R R J J R R J R J R 6 J J J R R J R J R J J R R 1. Reflect the point for alance Rock over the line for Summit Trail. Connect this point and verlook. The trails will connect at the intersection of the segment and Summit Trail. 15. Reflect point D over the mirrored wall. Connect this point and C. The intersection of the segment and the wall is the point to focus the camera. J J J R R R R J Geometr Chapter 9 195

6 nswers for Lesson 9-, pp Eercises (cont.) S-Isomer. nswers ma var. Sample: scissors, a baseball glove, a guitar. (, ) has image (, ). 5. (, ) has image (, ). 6. (, ) has image (, ). 7. a. b. nswers ma var. Sample: His writing hand would not cover what was written so far. 8. (0, 6) 9. (, 0) 0. (0, 0) 1. (, 6). (, 6). (0, ). (a, b) 5. (0, a) 6. (b,0) Leonardo da Vinci was left-handed. 7. rr; C rcr; C rcr; S ; S ; C S C ; ; ; C C Geometr Chapter 9 196

7 nswers for Lesson 9-, pp Eercises (cont.) 8 5. nswers ma var. Samples are given. 8. es; reflect a across an side and then reflect the image across the # bisector of that side. 9. es; follow Eercise 8 steps, first using one side of the triangle and again using a second side. 0. es; reflect a scalene across an side, a non-rt. isosc. across either leg, or a non-isosc. rt. across its hp. 1. es; reflect an isosc. across its base.. es; follow Eercise 8 using a rt. and the hp. as the first reflection line.. es; reflect an isosc. rt. across its hp.. The slope of is b a 1(a b) 1. The slope of is 1. Since (1)( 1) 1, the lines are #. The midpoint of,, which is a pt. on. 5. for b d, ; for b d, a 1 c 6. a. (, ) b. (, ) c. (, ) d. (, ) * ) Qd a c b R a b Q b 1 a e. The are the same point. a b a 1 b R a 1 b c d (d b) Geometr Chapter 9 197

8 nswers for Lesson 9-, pp Eercises 1.. E R E C D D R T C T.. K M T K S E I E M I S K J J K T R D D K J J K J K K J R Geometr Chapter 9 198

9 nswers for Lesson 9-, pp Eercises (cont.) H K 11. M J J 1. C 1. C K LM 16. I 17. K ; ; Y Y. Z X X Z. Y. X Z Z X Y Y X X Z X Z X X Y Z Z Y Y Z Y Y X Z Geometr Chapter 9 199

10 nswers for Lesson 9-, pp Eercises (cont.) 5. Y Y X X Z Z 6. MN MrNr; EN ENr; ME MrE; M M ; N N ; MEN M EN ; MEM NEN rotation about its center a c. d. Square; all sides are and all ' are 90. C D. Draw two segments connecting preimage pts. and to image pts. and. Construct the # bis. of r and r to find C, the center of rotation. m C is the of rotation.. nswers ma var. Sample: a 90 and a 70 rotation. Check students graphs. Rotation about origin: L (1, ), M (, 6), N (, ) Rotation about L: L (, 1), M (, ), N ( 1, 1) Rotation about M: L (5, 6), M (6, ), N (, ) Rotation about N: L (7, 0), M (8, ), N (, ) Geometr Chapter 9 00

11 nswers for Lesson 9-, pp Eercises 1. line; rotational: 180. line. rotational: 90. line, rotational: rotational: no smmetr 7. no smmetr 8. rotational: an angle; line: an line passing through the center 9. rotational: line 11. line, rotational: line, rotational: Geometr Chapter 9 01

12 nswers for Lesson 9-, pp Eercises (cont.) 17. rotational and reflectional 18. reflectional nswers ma var. Samples are given. 19. CDE, HD, DCK 0. TMT, HX, WXY 1. a. Language Horz. Vert. oint line line English, C, D, E,, H, I, M, H, I, N, H, I, K,, X, T, U, V, S, X, Z W, X, Y Greek, E, H, ˇ, Î, H, Z, H, ˇ, I, I, K, Ô,, ˇ, I, L, N, Ô,, Í, Ï, X M, Ô,, Ï, X, T, Á, Ï, X, Ç, b. nswers ma var. Sample: Greek; Greek alphabet has more letters with at least one kind of smmetr and more letters with multiple smmetries.. Sketches ma var.. reflectional. rotational: 90 ; reflectional. nswers ma var. Sample: 0 10 ; u 8 1 u u 1 8 u, ; reflectional; rotational 6. reflectional 7. point 8. none 9. reflectional; rotational 0. reflectional 1. reflectional, rotational. reflectional. Yes; the bisector divides the into ' with one side of the being the reflection of the other.. Not necessaril; the would need the two other ' to be. Geometr Chapter 9 0

13 nswers for Lesson 9-, pp Eercises (cont.) 5. Not necessaril; the bisector divides the segment into parts but one part cannot be the reflection of the other unless the bisector is the # bisector. 6. D 7. (, ) 8. (, ) 9. (, ) 0. (, ) 1. point smmetr about an pt. on the line; reflectional in an member of the famil of lines b. reflectional in -ais. reflectional in -ais. rotational smmetr of an about the origin; reflectional in an line through the origin 5. reflectional in Geometr Chapter 9 0

14 nswers for Lesson 9-, pp Eercises (cont.) 6. point smmetr about origin 7. reflectional in -ais 8. reflectional in -ais nswers ma var. Samples are given Geometr Chapter 9 0

15 nswers for Lesson 9-5, pp Eercises 1. enlargement; center, scale factor. enlargement; center C, scale factor. enlargement; center R, scale factor. reduction; center K, scale factor 5. reduction; center L, scale factor 6. enlargement; center M, scale factor 7. reduction; center (0, 0), scale factor 8. enlargement; center (0, 0), scale factor 9. enlargement; center (0, 0), scale factor in in in ft 1. about 0.5 in. 15. (6, ), Q (6, 1), R (1, ) 9 6 Q 9 15 R 16. ( 50, 10), Q ( 0, 0), R (10, 0) Q R Geometr Chapter 9 05

16 nswers for Lesson 9-5, pp Eercises (cont.) Q,0 R,Q Q0, R, R, Q 9 Q 9 R R 18. D (, 10) 19. L ( 15, 0) 0. ( 9, ) 1. T (0, 18). M (0, 0). N ( 0., 0.7). F Q 1, R 5. Q 1 8, 15 1 R 6. Q 7. Q ( 9, 1), W (9, 15), T (9, ), R ( 6, ) 8. Q ( 6, 8), W (6, 10), T (6, ), R (, ) 9. Q,,W,,T,,R 1, 0. Q Q,1 R,W, R,T, R,R Q, 1. Q ( 1.8,.), W (1.8, ), T (1.8, 0.6), R ( 1., 0.6). Q (.7,.6), W (.7,.5), T (.7, 0.9), R ( 1.8, 0.9). Q ( 0, 0), W (0, 50), T (0, 10), R ( 0, 10). Q ( 00, 00), W (00, 500), T (00, 100), R ( 00, 100) 5. The image has side lengths 10 in. and measures Q6"6, " R Q R Q Q 5 R 5 Q Q 1 R 1 Q 1 1 R 1 R Geometr Chapter 9 06

17 nswers for Lesson 9-5, pp Eercises (cont.) 7. Q 8. Q M M N N 1 N 8 N Q Q 6 8 M M Q M Q N 1. Check students work.. Use a scale factor of.. I J 10; H J 1. HJ 1; I J HI ; I J 7.5 M 6. The perimeter is doubled but the area is multiplied b. 7. ; 60 N M N M 6 6 Q 8. 60, 60; the two triangles are similar, so corresponding angles are congruent. N 10 Q Geometr Chapter 9 07

18 nswers for Lesson 9-5, pp Eercises (cont.) 9. T 50. T T T 51. T T G cm 9 56 G 56. ft X I H I H 57. False; a dilation doesn t map a segment to a segment unless the scale factor is False; a dilation does not change orientation. 59. False; a dilation with a scale factor greater than 1 is an enlargement. 60. True; the image and preimage are similar, so the corresponding ' are. T T Geometr Chapter 9 08

19 nswers for Lesson 9-5, pp Eercises (cont.) 61. False; if the center of dilation is on the preimage, it is also on the image. 6. Each verte is 1 ft from the light. 6. Connect corresponding points and and and. Etend r and r until the intersect at the center of dilation. The scale factor is the length of rr divided b the length of. 6. a., c. b. (, 6), Q Q ( 9, 1), R ( 1, ) R R 8 Q 65. a. ( 1, ), Q (, ), R (, 1) 8 1 b. Each point of the is reflected in the origin, which is the point of reflection. Two figures are smmetrical with respect to a pt. if is the midpoint of each segment that connects two corr. points of the figures. 66. Construct small square D E F G so that DrGr is on C (with D between ) and G ), E is on, and F is inside C. Draw Fr to meet C at F. Through F construct the line 6 to C. Label its point of intersection with as E. Through E and F construct the lines # to C. Label their points of intersection with C as D and G respectivel. DEFG is the desired square. Geometr Chapter 9 09

20 nswers for Lesson 9-6, pp Eercises 1. rotation. translation. Neither; the figures do not have the same orientation.. F is translated down twice the distance between / and m. m 5. M is translated across line m twice the distance between / and m. 6. T is translated across line m twice the distance between / and m. 7. L is rotated clockwise about V is rotated clockwise about 15. m m m m Geometr Chapter 9 10

21 nswers for Lesson 9-6, pp Eercises (cont.) 9. m N is rotated clockwise about N 6 N N N N 6 N N 16. opp.; reflection 17. opp.; glide reflection 18. same; translation 19. same; rotation 0. same; rotation 1. same; translation. opp.; reflection. opp.; glide reflection N N N N N Geometr Chapter 9 11

22 nswers for Lesson 9-6, pp Eercises (cont.). glide reflection; (, ) S (, ) followed b refl. in 1 5. rotation; 180 about the pt., 0 6. C 7. dd isometries can be epressed as the composition of an odd number of reflections. Even isometries are the composition of an even number of reflections. 8. Check students work. 9. Yes; a rotation of followed b a rotation of is equivalent to a rotation of ( ). 0. No; eplanations ma var rotation; center C, of rotation glide reflection; (, ) S ( 11, ), 0 7. translation; (, ) S ( 9, ) 8. reflection; 0 9. reflection; 0. reflection; 1. rotation; center (, 0), of rotation 180. glide reflection; (, ) S (, ),. translation; (, ) S ( 11, ) 1. rotation; center (0, ), of rotation 180 Q 1 5. Sample: Translate the red R so that one point moves to its corresponding point on the blue R. Then reflect across a line passing through that point. R 7 Geometr Chapter 9 1

23 nswers for Lesson 9-6, pp Eercises (cont.) 6 8. nswers ma var. Samples are given. 6. If XY is reflected in line /, then / is the # bis. of XXr and YYr, so XXr 6 YYr and XX YY is an isosc. trap. Therefore XY > XrYr. 7. XXr 6 YYr and XXr > YYr, so XX Y Y is a ~. Therefore, XY > XrYr. 8. If XY is rotated about pt. R, then RX > RXr and RY > RYr. lso, m XRY m YRX m YRX m X RY, so XRY X RY. So XRY X RY b SS and XY XrYr b CCTC. 9. nswers ma var. Sample: Since a reflection moves a pt. in the direction # to the translation, the order does not matter. 50. No; eplanations ma var. Sample: If (1, 1) is reflected over the line and then the -ais, the image is (1, 1). If the reflections are reversed, the image is ( 1, 1). 51. (6, 5) 5. (, 8) 5. (, 6) 5. (, 1) Geometr Chapter 9 1

24 nswers for Lesson 9-7, pp Eercises 1. nswers ma var. Samples are given. 1. es; translation; two # rectangles. es; translation; two? and a rhombus with a flower in it. es; translation; four rectangles in a square shape. es; translation; from upper left corner, 5 rectangles down and full width 5. es 6. es 7. no 8. no 9. no 10. no 11. rotational, reflectional, glide reflectional, and translational 1. rotational, point, reflectional, glide reflectional, and translational 1. rotational, reflectional, glide reflectional, and translational 1. rotational and reflectional Geometr Chapter 9 1

25 nswers for Lesson 9-7, pp Eercises (cont.) 18. C nswers ma var. Samples are given regular polgon with more than 6 sides must have measures greater than 10, and at least polgons must meet at each verte. The sum of or more ' with measures greater than So the regular polgons are -, -, and 6-sided, since their int. measures divide 60.. no. es; 5. es; 6. es; 7. reflectional, glide reflectional, rotational, and translational 8. rotational, point, reflectional, glide reflectional, and translational Geometr Chapter 9 15

26 nswers for Lesson 9-7, pp Eercises (cont.) 9 9. Figures that tessellate * 5 7 olgons Regular olgons *if square 0. a c. Drawings ma var. Sample: D M (a) C N (b) (c) d. Yes, CD tessellates; the sum of the measures of the ' of a quad. is 60. Copies of the quad. can be arranged so that the four ' share a verte. The quad. fills the plane. 1. nswers ma var. Sample: Draw C. Locate M, the mdpt. of, and N, the mdpt. of C. Draw the images of C under 180 rotations about M and N. Draw the image of C under the translation that maps to C. nd wa: Draw C. Draw the reflection image of pt. C over, C. Now use the steps from E. 8 for quad. CC. Geometr Chapter 9 16