Practice For use with pages

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1 9. For use with pages Use the translation (, ) ( 6, 3).. What is the image of (3, )?. What is the image of (4, )? 3. What is the preimage of 9(, 7)? 4. What is the preimage of 9(3, )? The vertices of n are (, ), (4, ), and (, 4). Graph the image of the triangle using prime notation. 5. (, ) ( 3, 5) 6. (, ) ( 4, ) n 999 is the image of n after a translation. Write a rule for the translation. Then verif that the translation is an isometr Name the vector and write its component form. 9. J M 0. Use the point P(5, ). Find the component form of the vector that describes the translation to P9. Y X 9 9. R opright Holt Mcougal. ll rights reserved.. P9(, 0) 3. P9(8, 3) 4. P9(0, 4) 5. P9(5, 4) 4 Geometr hapter 9 Resource ook

2 9. continued For use with pages The vertices of n are (, ), (, 6), and (3, ). Translate n using the given vector. Graph n and its image. 6. 8, 7. 7, 3 Find the value of each variable in the translation a8 3 b 5d8 808 c 8 9. b 5 0 3c a8 38 opright Holt Mcougal. ll rights reserved. 0. Navigation hot air balloon is fling from point to point. fter the balloon travels 6 miles east and 3 miles north, the wind direction changes at point. The balloon travels to point as shown in the diagram. (0, 0) (4, ) (6, 3) (8, 8) N a. Write the component form for ### Y and ### Y. b. The wind direction changes and the balloon travels from point to point. Write the component form for ### Y. c. What is the total distance the balloon travels? d. Suppose the balloon went straight from to. Write the component form of the vector that describes this path. What is this distance? Geometr hapter 9 Resource ook 5

3 9. For use with pages Use the diagram to write a matri to represent the polgon.. n E. n F 3. Quadrilateral EF 4. Heagon EF F E dd or subtract. 5. f6 3g f 9g 6. F G F G 7. F G F G 8. f0.3.8g f0.6.7g 9 9. F G F G 4G F F G Find the image matri that represents the translation of the polgon. Then graph the polgon and its image. M N O P. F 5 3 6G F ; 5 units right and ; 6 units left and 3 units down 6 5G units up Multipl. 4.6G 5. F GF G G 7. f3 6gF5 0 3G G f4 3gF 6 G 4. f0.8 4gF 3 6. F GF F GF opright Holt Mcougal. ll rights reserved. 6 Geometr hapter 9 Resource ook

4 9. continued For use with pages Use the described translation and the graph of the image to find the matri that represents the preimage units right and 4 units up 0. units left and 3 units down E9 9. Matri Equation Use the description of a translation of a triangle to find the value of each variable. What are the coordinates of the vertices of the image triangle? F G F b c d 5 G F 5 r s 6G opright Holt Mcougal. ll rights reserved.. Office Supplies Two offices submit suppl Office lists. weekl planner costs $8, a chairmat 5 weekl planners costs $90, and a desk tra costs $5. Use matri multiplication to find the total cost of supplies 5 chair mats for each office. 0 desk tras 3. School Pla The school pla was performed on three evenings. The attendance on each evening is shown in the table. dult tickets sold for $5 and student tickets sold for $3.50. Night dults Students First Second Third a. Use matri addition to find the total number of people that attended each night of the school pla. b. Use matri multiplication to find how much mone was collected from all tickets each night. Office 5 weekl planners 6 chair mats 30 desk tras Geometr hapter 9 Resource ook 7

5 9.3 For use with pages 64 6 Graph the reflection of the polgon in the given line.. -ais. -ais Graph the reflection of the polgon in the given line. Use the distance formula to show the figure and image are congruent Use matri multiplication to find the image. Graph the polgon and its image. in the -ais G 7. Reflect F G in the -ais. 8. Reflect F 5 7 opright Holt Mcougal. ll rights reserved. 8 Geometr hapter 9 Resource ook

6 Name ate 9.3 continued For use with pages 64 6 Write a matri for the polgon. Then find the image matri that represents the polgon after a reflection in the given line. 9. -ais 0. -ais. -ais Find point on the -ais so is a minimum.. (, ), (, 4) 3. (, 4), (6, 3) 4. (3, ), (6, 4) The vertices of n are (, ), (3, 4), and (3, ). Reflect n in the first line. Then reflect n 999 in the second line. Graph n 999 and n In 5, then in 5 6. In 5 4, then in 5 7. In 5, then in 5 opright Holt Mcougal. ll rights reserved. 8. Laing able Underground electrical cable is being laid for two new homes. Where along the road (line m) should the transformer bo be placed so that there is a minimum distance from the bo to each of the homes? 4 Geometr hapter 9 Resource ook 9

7 9.4 For use with pages Match the diagram with the angle of rotation Trace the polgon and point P on paper. Then draw a rotation of the polgon the given number of degrees about P P P P Rotate the figure the given number of degrees about the origin. List the coordinates of the vertices of the image. Show that the figure and image are congruent Find the value of each variable in the rotation s 3 4s opright Holt Mcougal. ll rights reserved. r 0 Geometr hapter 9 Resource ook

8 9.4 continued For use with pages Find the image matri that represents the rotation of the polgon about the origin. Then graph the polgon and its image. 3. F 4 3 4G ; F G ; F G F ; G ; 708 opright Holt Mcougal. ll rights reserved. The endpoints of } are (, ) and (4, 5). Graph } 99 and } 00 after the given rotations. 7. Rotation: 908 about the origin 8. Rotation: 808 about the origin Rotation: 708 about (, 0) Rotation: 908 about (0, 3) 4 Geometr hapter 9 Resource ook

9 9.5 For use with pages The endpoints of } are (, ) and (5, 4). Graph the image of } after the glide reflection.. Translation: (, ) ( 4, ). Translation: (, ) (, ) Reflection: in the -ais Reflection: in 5 The vertices of n are (3, ), (, 5), and (5, 3). Graph the image of n after a composition of the transformations in the order the are listed. 3. Translation: (, ) ( 3, 5) 4. Translation: (, ) ( 6, ) Reflection: in the -ais Rotation: 908 about the origin Graph } F 0G0 after a composition of the transformations in the order the are listed. Then perform the transformations in reverse order. oes the order affect the final image } F 0G0? 5. F(4, 4), G(, ) 6. F(, 3), G(4, ) Rotation: 908 about the origin Reflection: in the line 5 Reflection: in the -ais Translation: (, ) (, 0) opright Holt Mcougal. ll rights reserved. Geometr hapter 9 Resource ook

10 9.5 continued For use with pages Verif that the figures are congruent b describing the composition of transformations In the diagram, k i m, } is reflected in line k, and } 99 is reflected in line m. 9. translation maps } onto which segment? 0. Which lines are perpendicular 0?. Name two segments parallel to } 0.. If the distance between k and m is.7 centimeters, what is the length of } 0? 3. Is the distance from 9 to m the same as the distance from 0 to m? Eplain k m Find the angle of rotation that maps onto 0. opright Holt Mcougal. ll rights reserved m k 6. Stenciling a order The border pattern below was made with a stencil. escribe how the border was created using one stencil four times m k Geometr hapter 9 Resource ook 3

11 FOUS ON 9.5 For use with pages oes the shape tessellate? If so, tell whether the tessellation is regular.. Right triangle. Irregular heagon 3. Parallelogram Use the steps in Eample to make a figure that will tessellate. 4. Make a tessellation using a square as the base figure. 5. Make a tessellation using a heagon as the base figure. hange one pair of opposite sides. 6. Make a tessellation using a trapezoid as the base figure. hange both pairs of opposite sides. Verif that a tessellation can be made using the given polgons escribe the transformation(s) used to make the tessellation hallenge Tessellations occur often in the real world, especiall in nature. bee s honecomb is a tessellation of heagons. brick wall is a tessellation of rectangles. Think of one eample of a real-world tessellation and draw it. opright Holt Mcougal. ll rights reserved. 4 Geometr hapter 9 Resource ook

12 9.6 For use with pages etermine whether the figure has rotational smmetr. If so, describe the rotations that map the figure onto itself oes the figure have the rotational smmetr shown? If not, does the figure have an rotational smmetr? opright Holt Mcougal. ll rights reserved. In Eercises 6, draw a figure for the description. If not possible, write not possible.. triangle with eactl two lines. quadrilateral with eactl two lines of smmetr of smmetr 3. pentagon with eactl two lines 4. heagon with eactl two lines of smmetr of smmetr Geometr hapter 9 Resource ook 5

13 9.6 continued For use with pages n octagon with eactl two lines 6. quadrilateral with eactl four lines of smmetr of smmetr 7. Paper Folding piece of paper is folded in half and some cuts are made, as shown. Which figure represents the piece of paper unfolded?.... In Eercises 8 and 9, use the following information. Taj Mahal The Taj Mahal, located in India, was built between 63 and 653 b the emperor Shah Jahan as a monument to his wife. The floor map of the Taj Mahal is shown. 8. How man lines of smmetr does the floor map have? 9. oes the floor map have rotational smmetr? If so, describe a rotation that maps the pattern onto itself. In Eercises 0 and, use the following information. rains Refer to the diagram below of a drain in a sink. 0. oes the drain have rotational smmetr? If so, describe the rotations that map the image onto itself.. Would our answer to Eercise 0 change if ou disregard the shading of the figures? Eplain our reasoning. opright Holt Mcougal. ll rights reserved. 6 Geometr hapter 9 Resource ook

14 9.7 For use with pages Find the scale factor. Tell whether the dilation is a reduction or an enlargement. Then find the values of the variables.. P9 5 P P9 P 6 Use the origin as the center of the dilation and the given scale factor to find the coordinates of the vertices of the image of the polgon. 3. k k 5 } 3 M N G L I H 5. k 5 6. k 5 5 } opright Holt Mcougal. ll rights reserved. dilation maps to 9 and to 9. Find the scale factor of the dilation. Find the center of the dilation. 7. (4, ), 9(5, ), (0, 6), 9(8, 3) 8. (, 6), 9(3, ), (, ), 9(6, 0) R P S 9. (3, 6), 9(6, 3), (, 0), 9(8, 4) 0. (4, ), 9(5, 3), (, 0), 9(, ) Geometr hapter 9 Resource ook 7

15 9.7 continued For use with pages The vertices of ~ are (, ), (3, 5), (, 5), and (9, ). Graph the image of the parallelogram after a composition of the transformations in the order the are listed.. Translation: (, ) ( 5, ) ilation: centered at the origin with a scale factor of 3 } 5. ilation: centered at the origin with a scale factor of Reflection: in the -ais 4 In Eercises 3 5, use the following information. Flashlight Image You are projecting images onto a wall with a flashlight. The lamp of the flashlight is 8.3 centimeters awa from the wall. The preimage is imprinted onto a clear cap that fits over the end of the flashlight. This cap has a diameter of 3 centimeters. The preimage has a height of centimeters and the lamp of the flashlight is located.7 centimeters from the preimage. 3. Sketch a diagram of the dilation. 4. Find the diameter of the circle of light projected onto the wall from the flashlight. 5. Find the height of the image projected onto the wall. opright Holt Mcougal. ll rights reserved. 8 Geometr hapter 9 Resource ook