_.1 ractice 1. Name the vector and write its component form. K J. The vertices of, 3, 1,, and 0, 1. Translate using the vector 1,. Graph and its image. are ( ) ( ) ( ) 3. Find the component form of the vector that translates ( ) ( ) 3, to 1,.. Write a rule for the translation of RST to R ST. S R S T R T 6 In Eercises 5 and 6, use the translation (, ) ( 1, 3) of the given point. 5. Q ( 5, 9) 6. M ( 3, ) + to find the image with vertices ( ) ( ) ( ) In Eercises 7 and, graph DE 1, 3, D 0,, and E 1, 1 and its image after the given translation or composition. 7. Translation: (, ) ( 3, + 1). Translation: (, ) ( + 10, ) Translation: (, ) ( 7, + 15) 9. You want to plot the collinear points (, 3 ), (, ), and ( 3, 7) on the same coordinate plane. Do ou have enough information to find the values of and? Eplain our reasoning. 10. You are using the map shown to navigate through the cit. You decide to walk to the ost Office from our current location at the ommunit enter. Describe the translation that ou will follow. If each grid on the map is 0.05 mile, how far will ou travel? 3 ommunit enter 1 ost Office 0 0 1 3 opright ig Ideas Learning, LL Geometr Resources b hapter 111
.1 ractice 1. The vertices of FGH are F( ) G( ) H( ) using the vector, 7. Graph FGH and its image., 6, 3, 0, and 1,. Translate FGH. Find the component form of the vector that translates ( ) ( ), to 7, 9. 3. Write a rule for the translation of to. In Eercises and 5, use the translation (, ) (, 3) image of the given point. + to find the. G(, ) 5. H ( 10, 5) 6. Graph JKL composition. with vertices J(, ), K( 1, 3 ), and L( 5, ) Translation: (, ) ( + 6, 1) Translation: (, ) ( 1, 7) and its image after the 7. Is the transformation given b (, ) (, 1) our reasoning. + + a translation? Eplain. popular kid s game has 15 tiles and 1 open space. The goal of the game is to rearrange the tiles to put them in order (from least to greatest, starting at the upper left-hand corner and going across each row). Use the figure to write the transformation(s) that describe the path of where the tile is currentl, and where it must be b the end of the game. an this same translation be used to describe the path of all the tiles? 3 7 5 6 1 1 9 13 11 15 10 1 9. Graph an triangle and translate it in an direction. Draw translation vectors for each verte of the triangle. Is there a geometric relationship between all the translation vectors? Eplain wh this makes sense in terms of the slope of the line. 10. oint (, ) undergoes a translation given b (, ) ( 3, a), another translation (, ) ( b, + 7) to produce the image of ( ) the values of a and b and point. + followed b 5,. Find 11 Geometr opright ig Ideas Learning, LL Resources b hapter
. ractice In Eercises 1 3, graph 1. ( ) ( ) ( ) 0,, 1, 3,, ; -ais. ( ) ( ) ( ),, 6,, 3, 5 ; -ais, 1, 3,, 1, 1 ; = 3. ( ) ( ) ( ) and its image after a reflection in the given line. In Eercises and 5, graph the polgon and its image after a reflection in the given line.. = 5. = Q R S S R Q In Eercises 6 and 7, graph JKL its image after the glide reflection. with vertices J(, 3 ), K(, 1 ), and L( 1, 5) and 6. Translation: (, ) ( 1, ) 7. Translation: (, ) ( +, 3) Reflection: in the -ais Reflection: in the line = In Eercises and 9, determine the number of lines of smmetr for the figure.. 9. 10. Find point W on the -ais so that VW XW X (, 1 ). + is a minimum given V (, 3) 11. line = 3 5 is reflected in = a so that the image is given b = 1 3. What is the value of a? 1. Your friend claims that it is not possible to have a glide reflection if ou have two translations followed b one reflection. Is our friend correct? Eplain our reasoning. and 116 Geometr opright ig Ideas Learning, LL Resources b hapter
_. ractice In Eercises 1 and, graph DE and its image after a reflection in the given line. 1. ( 3, ), D(, 1 ), E( 0, 5 ); -ais. ( ) ( ) ( ) 1, 6, D 1,, E 7, ; = In Eercises 3 and, graph the polgon and its image after a reflection in the given line. 3. -ais. = 1 L 6 K N K N M L M In Eercises 5 and 6, graph its image after the glide reflection. with vertices ( 1, ), (, 1 ), and (, 3) and 5. Translation: (, ) ( +, 1) 6. Translation: (, ) ( 3, + 1) Reflection: in the line = Reflection: in the line = 7. Determine the number of lines of smmetr. Find point on the -ais so that for the figure. + is a minimum. 9. Is it possible to perform two reflections of an object so that the final image is identical to the original image? If so, give an eample. If not, eplain our reasoning. 10. triangle undergoes a glide reflection. Is it possible for the sides of the triangle to change length during this process? Eplain our reasoning. 11. Your friend claims that it is not possible to have a glide reflection if ou have one translation followed b two reflections. Is our friend correct? Eplain our reasoning. opright ig Ideas Learning, LL Geometr Resources b hapter 117
_.3 ractice 1. Trace the polgon and point. Then draw a 60 rotation of the polgon about point. D. Graph the polgon and its image after a 70 rotation about the origin. J M K In Eercises 3 and, graph RST and its image after the composition. 3. Translation: (, ) (, 1) with vertices R(, 3 ), S(, 1 ), and T( 1, 5). Reflection: in the line = Rotation: 90 about the origin Rotation: 10 about the origin In Eercises 5 and 6, determine whether the figure has rotational smmetr. If so, describe an rotations that map the figure onto itself. 5. 6. L 7. Draw with points (, 0 ) and ( 0, ). Rotate the segment 90 counterclockwise about point. Then rotate the two segments 10 about the origin. What geometric figure did ou create using the original segment and its images?. List the uppercase letters of the alphabet that have rotational smmetr, and state the angle of the smmetr. opright ig Ideas Learning, LL Geometr Resources b hapter 11
.3 ractice 1. Graph the polgon and its image after a 90 rotation about the origin. W U T V with vertices ( ) ( ) ( ) In Eercises and 3, graph DE 1, 3, D,, and E 5, 1 and its image after the composition.. Rotation: 10 about the origin 3. Reflection: in the line = Translation: (, ) ( 3, 1) + + Rotation: 70 about the origin In Eercises and 5, determine whether the figure has rotational smmetr. If so, describe an rotations that map the figure onto itself.. 5. 6. Is it possible to have an object that does not have 360 of rotational smmetr? Eplain our reasoning. 7. figure that is rotated 60 is mapped back onto itself. Does the figure have rotational smmetr? Eplain. How man times can ou rotate the figure before it is back where it started?. Your friend claims that he can do a series of translations on an geometric object and get the same result as a rotation. Is our friend correct? 9. Your friend claims that she can do a series of reflections on an geometric object and get the same result as a rotation. Is our friend correct? 10. List the digits from 0 9 that have rotational smmetr, and state the angle of the smmetr. 1 Geometr opright ig Ideas Learning, LL Resources b hapter
. ractice In Eercises 1 and, identif an congruent figures in the coordinate plane. Eplain. 1.. 6 6 7 3 6 1 7 5 6 6 10 1 6 9 6 5 3 In Eercises 3 and, describe a congruence transformation that maps to. 3.. 6 In Eercises 5 and 6, determine whether the polgons with the given vertices are congruent. Use transformations to eplain our reasoning. 5. ( 5, ), (, ), (, 7 ) and S(, 5 ), T( 1, 5 ), U( 1, 0) 6. E( 6, ), F( 10, ), G( 10, ), H( 6, ) and W(, ), X(, 10 ), Y(, 10 ), Z(, ) 7. In the figure, a b, DE is reflected in line a, and DE is reflected in line b. List three pairs of segments that are parallel to each other. Then determine whether an segments are congruent to EE. In Eercises and 9, find the measure of the acute or right angle formed b intersecting lines so that can be mapped to using two reflections.. rotation of maps to. 9. The rotation ( ) ( ),, maps to. D D E E a b D E 16 Geometr opright ig Ideas Learning, LL Resources b hapter
_.5 ractice In Eercises 1 and, find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. 1.. 9 7 10 In Eercises 3 5, cop the diagram. Then use a compass and straightedge to construct a dilation of quadrilateral D with the given center and scale factor k. 3. enter, k = 3 D. enter, k = 1 5. enter, k = 75% In Eercises 6 and 7, graph the polgon and its image after a dilation with a scale factor k. 1,, Q,, R,, S 1, 3 ; k = 6. ( ) ( ) ( ) ( ),,, 6, 1, 1, D, ; k = 75% 7. ( ) ( ) ( ) ( ). standard piece of paper is.5 inches b 11 inches. piece of legal-size paper is.5 inches b 1 inches. what scale factor k would ou need to dilate the standard paper so that ou could fit two pages on a single piece of legal paper? 9. The old film-stle cameras created photos that were best printed at 3.5 inches b 5 inches. Toda s new digital cameras create photos that are best printed at inches b 6 inches. Neither size picture will scale perfectl to fit in an 11-inch b 1-inch frame. Which tpe of camera will ou minimize the loss of the edges of our picture? 10. Your friend claims that if ou dilate a rectangle b a certain scale factor, then the area of the object also increases or decreases b the same amount. Is our friend correct? Eplain our reasoning. 1 in..5 in. 11. Would it make sense to state dilation has a scale factor of 1? Eplain our reasoning. opright ig Ideas Learning, LL Geometr Resources b hapter 131
.5 ractice In Eercises 1 and, find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. 1.. 9 1.5 1 In Eercises 3 and, cop the diagram. Then use a compass and straightedge to construct a dilation with the given center and scale factor k. D 3. enter, k =. enter, k = 75% In Eercises 5 and 6, graph the polgon and its image after a dilation with a scale factor k. J 3,, K, 1, L 3,, M 5, ; k = 50% 5. ( ) ( ) ( ) ( ) V 1, 1, W 1, 0, X,, Y 3,, Z 0, 3; k = 3 6. ( ) ( ) ( ) ( ) ( ) 7. You look up at the sk at night and see the moon. It looks like it is about millimeters across. If ou then look at the moon through a telescope that has a magnification of 0 times, how big will it look to ou through the telescope?. What would it mean for an object to be dilated with a scale factor of k = 0? 9. Your friend claims that if ou dilate a rectangle b a certain scale factor, then the perimeter of the object also increases or decreases b the same factor. Is our friend correct? Eplain our reasoning. 10. The image shows an object that has been dilated with an unknown scale factor. Use the given measures to determine the scale factor and solve for the value of. 3 + 16 13 Geometr opright ig Ideas Learning, LL Resources b hapter
.6 ractice In Eercises 1 and, graph QR with vertices ( 1, 5 ), Q(, 3 ), and R(, 1) and its image after the similarit transformation. 1. Rotation: 10 about the origin. Dilation: (, ) ( 1, 1 ) Dilation: (, ) (, ) Reflection: in the -ais 3. Describe a similarit transformation that maps the black preimage onto the dashed image. X W W X Y Z Z Y In Eercises and 5, determine whether the polgons with the given vertices are similar. Use transformations to eplain our reasoning.. (, 5 ), (, ), ( 1, ) and 5. J( ) K( ) L( ) M( ) D( 3, 3 ), E( 3, 1 ), F(, 1) T( 3, 3, ) U(, 3, ) V(,, ) W( 3, 1) 5, 3, 3, 1, 3, 5, 5, 5 and 6. rove that the figures are similar. Given Equilateral GHI with side length a, rove equilateral QR with side length b GHI is similar to QR. I G a H b Q R 7. Your friend claims ou can use a similarit transformation to turn a square into a rectangle. Is our friend correct? Eplain our answer.. Is the composition of a dilation and a translation commutative? In other words, do ou obtain the same image regardless of the order in which the transformations are performed? Justif our answer. 9. The image shown is known as a Sierpinski triangle. It is a common mathematical construct in the area of fractals. What can ou sa about the similarit transformations used to create the white triangles in this image? 136 Geometr opright ig Ideas Learning, LL Resources b hapter