Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved O 13. (-6, 4) 14. (-8, 0) 15.

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1 hapter 9 nswers earson ducation, nc., publishing as earson rentice Hall. ll rights reserved. ractice o; the triangles are not the same size.. Yes; the hexagons are the same shape and size. 3. Yes; the ovals are the same shape and size. a. and F b. D and D, D and D, F and F, F and F 5a. M and 5b. M and M, and, M and M. (x, ) (x -, - ) 7. (x, ) (x -, - ) (x, ) (x - 3, - 1) (x, ) (x +, - ) 10. (x, ) (x - 5, + 1) (x, ) (x +, + ) 1. W (-, ), (-1, ), Y (3, 3), (, 1) 13. J (-5, 0), K (-3, ), (-3, -) 1. M (3, -), (, -), (7, -7), (, -) 1 (x, ) (x +., + ) 1. (x, ) (x + 13, - 13) 17. (x, ) (x,) 1 (x, ) (x + 3, + 3) 19a. (-3, -1) 19b. (0, 8), (-5, ), (, 3) ractice 9-1. (-3, -). (-, -3) 3. (-1, -). (, -) (, -1). (3, -) 7a. 7b. 8a. 8b. x J K K J x W Y W x (-, ) 1. (-8, 0) 1 (0, -1) ractice x x 8 8 x, GH G. 7. U x Y x U Geometr hapter 9 nswers 35

2 hapter 9 nswers (continued) ractice 9-1. he helmet has reflectional smmetr.. he teapot has reflectional smmetr. 3. he hat has both rotational and reflectional smmetr.. he hairbrush has reflectional smmetr ' ' M M ' ' ' ' M M M 7. his figure has no lines of smmetr line smmetr line smmetr and 7 rotational smmetr line smmetr and 90 rotational smmetr line smmetr and 5 rotational smmetr 180 rotational smmetr line smmetr earson ducation, nc., publishing as earson rentice Hall. ll rights reserved. 3 nswers Geometr hapter 9

3 hapter 9 nswers (continued) line smmetr and 5 rotational smmetr earson ducation, nc., publishing as earson rentice Hall. ll rights reserved line smmetr rotational smmetr ractice (-, -), M (-1, 0), (, -1), (0, -1). (-30, -30), M (-15, 0), (30, -15), (0, -15) 3. (-1, -1), M (-, 0), (1, -), (0, -) es no no 10. K H (-1, -1), (-, 0), (0, -) 1. (-, ), (1,- ), (1,) 1 (-1, ), (3, ), (-, ) 1. (-, 1), (-1, 0), (0, 1) ractice D.. V..... V. D 3... J J m m m J x m m Geometr hapter 9 nswers 37

4 hapter 9 nswers (continued) x x x x 8 x x x 1. reflection 1 rotation 1. glide reflection 17. translation ractice translational smmetr line smmetr, rotational smmetr, translational smmetr, glide reflectional smmetr translational smmetr line smmetr, rotational smmetr, translational smmetr, glide reflectional smmetr line smmetr, rotational smmetr, translational smmetr, glide reflectional smmetr rotational smmetr, translational smmetr earson ducation, nc., publishing as earson rentice Hall. ll rights reserved. 38 nswers Geometr hapter 9

5 hapter 9 nswers (continued) amples: 10. Y Z earson ducation, nc., publishing as earson rentice Hall. ll rights reserved. 1. es 13. es 1. no 1 es 1. no 17. no eteaching heck students work.. (0, -3), (1, 1), (, -1), D (5, -) 7. (, -), (5, ), (8, 0), D (9, -3) (3, 5), (, 9), (7, 7), D (8, ) eteaching 9-1. heck students work.. reflection across x-axis: F (-1, -3), G (-5, -1), H (-3, -5); reflection across -axis: F (1, 3), G (5, 1), H (3, 5) 7. reflection across x-axis: (, -), D (5, -), (, -3); reflection across -axis: (-, ), D (-5, ), (-, 3) reflection across x-axis: J (-1, 5), K (-, 3), (-, ); reflection across -axis: J (1, -5), K (, -3), (, -) eteaching Y Y 7. ample: Y Y Y Z Z eteaching 9-1. two lines of smmetr (vertical and horizontal), 180 rotational smmetr (point smmetr). one line of smmetr (horizontal) 3. one line of smmetr (vertical). two lines of smmetr (vertical and horizontal), 180 rotational smmetr (point smmetr) one line of smmetr (vertical). one line of smmetr (vertical) eteaching heck students work.. x 3. x x Y Z Geometr hapter 9 nswers 39

6 hapter 9 nswers (continued) eteaching 9-1. translation. reflection 3. rotation. glide reflection rotation. glide reflection 7. reflection translation eteaching ample: x line smmetr across the dashed lines, rotational smmetr around points, translational smmetr, glide reflectional smmetr line smmetr across the dashed lines, rotational smmetr around points, translational smmetr, glide reflectional smmetr line smmetr across the dashed lines, rotational smmetr around points, translational smmetr, glide reflectional smmetr nrichment (x, ) (x - 7, - ). (x, ) (x +, - 7) 3. (x, ) (x - 10, + 5). (x, ) (x - 3, - ) Foster. es 7. Wilson (x, ) (x - 7, - 3) nrichment 9-1. (-3, -1). (-1, 0) 3. (5, 3) x 1 1 x 1 1. the midpoint formula: M = (, ) 1 1. = x + 7. =- ' 0 ' J K 0 J' 8 K' ' x ' x ' earson ducation, nc., publishing as earson rentice Hall. ll rights reserved. rotational smmetr around points, translational smmetr 0 nswers Geometr hapter 9

7 hapter 9 nswers (continued) earson ducation, nc., publishing as earson rentice Hall. ll rights reserved. =-x D x = =-x - V' = 3x + M 8 0 ' ' ' M' 0 D D' 0 F U' W' ' 8 0 F' ' x ' ' ' x U D' x V x W 1. 1 =-x - 1 nrichment (0, -, 3). (-, -, 3) 3. (-, -, 0). (0, -, 0) (0, -, 0). (0, -, 3) 7. (-, -, 3) (-, -, 0) (, 0, 3) 10. (, -, 3) (, -, 0) 1. (, 0, 0) 13. (, 0, 0) 1. (, 0, 3) 1 (, -, 3) 1. (, -, 0) nrichment 9- G' H' 8 0 H G K' J' x 1. es; rotational and point smmetr. no 3. es; rotational and point smmetr. es; rotational and point smmetr no. no 7. diamonds 1 even of diamonds; this does not have smmetr because the diamond in the middle is toward either the bottom or top of the card, and when ou rotate the card 180, the position will be reversed. 10. ll the face cards have smmetr. es;,, o; ample: When ou look at the card one wa, three of the points of the hearts are pointing down, and five are pointing up. When ou rotate the card 180º, five of the points of the hearts are pointing down, and three are pointing up. 13. o; because the number and suit of each card are placed in opposite corners, none of the cards have line smmetr. 1. You can add a backward 3 with the small club below it to the two empt corners to create line smmetr, or ou can remove the 3 with the small club below it from each of the two corners. nrichment 9-5 1a. (, 0, ) 1b. (0, 0, ) 1c. (0,, ) 1d. (,, ) 1e. (, 0, 0) 1f. (0, 0, 0) 1g. (0,, 0) 1h. (,, 0) a. (, 0, ) b. (0, 0, ) c. (0,, ) d. (,, ) e. (, 0, 0) f. (0, 0, 0) g. (0,, 0) h. (,, 0) 3. (0, 0, 0). ach edge in the image is double that in the preimage.. amples: hree faces are coplanar for image and preimage; three faces are parallel; each face in the image has two times the perimeter and four times the area of the corresponding face in the preimage. 7. urface area of image = 9 sq. units; surface area of preimage = sq. units; the ratio of the surface areas is : 1. ' J K Geometr hapter 9 nswers 1

8 hapter 9 nswers (continued) Volume of image = cubic units; volume of preimage = 8 cubic units; the ratio of the volumes is 8 : 1. Dilations in three dimensions are proportional to dilations in two dimensions. nrichment 9-1. heck students work ; rotation; twice nrichment M G F hapter roject ctivit 1: nvestigating a. vertical b. vertical c. both ctivit : Modeling a. ncient gptian ornament b. riental design c. Greek vase design G D 7 F 3 F M M 15 G 5 M G M Y M M F 1 Y ctivit 3: nvestigating a, b ctivit : lassifing a. mg b. 1 ctivit 5: reating heck students work. heckpoint uiz 1 1. o; the figures are not the same size.. es 3. es. (x, ) (x - 3, - ) units right and units down. a resultant translation of units right and 11 units up 7. ', ' ' D D' 10. ( 8, -5), (, -3) and (, 0) heckpoint uiz 1. line smmetr; rotational; 180. line smmetr; rotational; line smmetr ' H. rotational; 180 translational; no turns. rotational; preimage turns 7. translational rotational, reflectional, translational translational hapter est, Form 1. (13, 0), (10, -), (11, -), (13, -). (-1, -), (, -), (1, -), (-1, -8) 3. (0, -5), (, -), (, -3), (, -5). (-.5, 0), (-1, -1), (-1.5, -), (-.5, -3) (5, ), (, 0), (3, -), (5, -). (-11, 3), (-8, 1), (-9, -1), (-11, -3) 7. glide reflection translation translation 10. rotation ' D' ' D ' earson ducation, nc., publishing as earson rentice Hall. ll rights reserved. nswers Geometr hapter 9

9 hapter 9 nswers (continued) 1. ' earson ducation, nc., publishing as earson rentice Hall. ll rights reserved. 1. line smmetr 13. rotational smmetr 1a. n two of the following: DHKMUVWY 1b. n two of the following: HZ 1 ranslations can be performed on the pieces because the can slide. otations can be performed on the pieces because each piece can be turned. eflections and glide reflections cannot be performed on the pieces because the back of a puzzle piece is useless in solving the puzzle. Dilations are impossible because the pieces cannot change size ample: glide reflectional, rotational, line, and translational (-3, ), M (, ), (3, -9) 1 (, - ), M (,1), (, - ) 0. (-18, -18), M (-18, 18), 5 7 (0, 0) 1. (3, -), M (0, - 3 ), ( 3, -) 3. Y = 15 cm; = cm; scale factor = Y = 5 in.; Y = 0 in.; scale factor = 3. (-1, 3) (5, ). (-, -7) 7. (, -7) (1, -1) (-3, 1) hapter est, Form 1. Yes; the figures are the same shape and size.. o; the figures are not the same size. 3. Yes; the figures are the same shape and size.. (x, ) (x -, + 1) (x, ) (x + 3, - 7). 9(0, -3), 9(-, 0), 9(-, -), D9(-3, -5) 7. 9(, 3), 9(10, 0), 9(1, ), D9(9, 5) 9(3, 8), 9(-1, 5), 9(-3, 9), D9(0, 10) 9(5, ), 9(1, -1), 9(-1, 3), D9(, ) 10. 9(-3, 0), 9(0, -), 9(-, -), D9(-5, -3) 9(0, 3), 9(, ), 9(, ), D9(3, 1) 1. (x, ) (x +, - 3) 13. (x, ) (x - 3, + ) 1. rhombus and two triangles; translation 1 ' ' ' ' ' rotational smmetr 1 line smmetr 1 line smmetr; 180 rotational smmetr 0. (-7, 0) 1. (0, -3). (-, 1) 3. (-9, -). (, -) (-5, 11) lternative ssessment, Form K 1: coring Guide 0; 00 cm; all distances are magnified 0 times. 3 tudent gives correct answers and a clear and accurate explanation. tudent gives answers and an explanation that are largel correct. 1 tudent gives answers or an explanation that ma contain serious errors. 0 tudent makes little or no effort. K : coring Guide ample: 3 tudent draws a figure that accuratel reflects the stated conditions. tudent draws a figure that is mostl correct but falls just short of satisfing all the stated conditions. 1 tudent draws a figure that has significant flaws relative to the stated conditions. 0 tudent makes little or no effort. Geometr hapter 9 nswers 3

10 hapter 9 nswers (continued) K 3: coring Guide ample: he car can undergo translations and rotations as it moves and turns. ut it can undergo neither a dilation, which would change its size, nor a reflection, which would, for example, put the steering wheel on the passenger side. 3 tudent gives a correct and thorough explanation. tudent gives an explanation that demonstrates understanding of transformations but ma contain minor errors or omissions. 1 tudent gives an explanation containing major errors or omissions. 0 tudent makes little or no effort. K : coring Guide ample: a. translation: b. dilation: c. reflection: x x x x translation vector: 1, 0 scale factor: line of reflection: = 1 d. glide reflection: e. rotation: he glide reflection is equivalent to a translation, 0 followed b a reflection across the line =-. degrees of rotation: 90 3 tudent gives accurate graphs and correctl identifies the details the problem calls for. tudent gives generall correct graphs and details, although the work ma contain some errors. 1 tudent gives graphs and accompaning details that contain significant errors or omissions. 0 tudent makes little or no effort. umulative eview 1. D. G 3.. H. J 7. H 10. J 1. H J cm 3 17., H,, M,,, U, V, W,, Y 1 otational; it is turning around a fixed point, the corner quilateral triangle, square, and regular hexagon; the measure of each interior angle is a factor of f a triangle is not a right triangle, then the thagorean heorem cannot be applied.. V V U U x W W x x x U G U G earson ducation, nc., publishing as earson rentice Hall. ll rights reserved. nswers Geometr hapter 9