Transformations and Similarity

Transcription

1 Transformations and Similarit? MDULE 10 LESSN 10.1 ESSENTIL QUESTIN Properties of Dilations How can ou use dilations and similarit to solve real-world problems? 8.G.3, 8.G. LESSN 10. lgebraic Representations of Dilations 8.G.3 LESSN 10.3 Similar Figures Houghton Mifflin Harcourt Publishing ompan 8.G. Real-World Video m.hrw.com m.hrw.com To plan a mural, the artist first makes a smaller drawing showing what the mural will look like. Then the image is enlarged b a scale factor on the mural canvas. This enlargement is called a dilation. m.hrw.com Math n the Spot nimated Math Personal Math Trainer Go digital with our write-in student edition, accessible on an device. Scan with our smart phone to jump directl to the online edition, video tutor, and more. Interactivel eplore ke concepts to see how math works. Get immediate feedback and help as ou work through practice sets. 313

2 re YU Read? omplete these eercises to review skills ou will need for this module. Simplif Ratios EXMPLE 35 1 = = _ 5 3 Write each ratio in simplest form. m.hrw.com Personal Math Trainer nline Practice and Help To write a ratio in simplest form, find the greatest common factor of the numerator and denominator. Divide the numerator and denominator b the GF Multipl with Fractions and Decimals EXMPLE 3 _ 5 0 = = = 5 Write numbers as fractions and multipl. Simplif Multipl as ou would with whole numbers. Place the decimal point in the answer based on the total number of decimal places in the two factors. Multipl _ 9 Graph rdered Pairs (First Quadrant) EXMPLE 10 5 Graph each point on the coordinate grid above Graph the point (, 3.5). Start at the origin. Move units right. Then move 3.5 units up. Graph point (, 3.5). Houghton Mifflin Harcourt Publishing ompan 9. (9, 0) 10. (, 7) 11. D (0,.5) 1. E (,.5) 31 Unit

3 Reading Start-Up Visualize Vocabular Use the words to complete the graphic organizer. You will put one word in each rectangle. The four regions on a coordinate plane. The horizontal ais of a coordinate plane. Understand Vocabular Reviewing the oordinate Plane omplete the sentences using the preview words. The point where the aes intersect to form the coordinate plane. The vertical ais of a coordinate plane. Vocabular Review Words coordinate plane (plano cartesiano) image (imagen) origin (origen) preimage (imagen original) quadrants (cuadrante) ratio (razón) scale (escala) -ais (eje ) -ais (eje ) Preview Words center of dilation (centro de dilatación) dilation (dilatación) enlargement (agrandamiento) reduction (reducción) scale factor (factor de escala) similar (similar) 1. figure larger than the original, produced through dilation, is an.. figure smaller than the original, produced through dilation, is Houghton Mifflin Harcourt Publishing ompan a. ctive Reading Ke-Term Fold efore beginning the module, create a ke-term fold to help ou learn the vocabular in this module. Write the highlighted vocabular words on one side of the flap. Write the definition for each word on the other side of the flap. Use the ke-term fold to quiz ourself on the definitions used in this module. Module

4 GETTING REDY FR Transformations and Similarit Understanding the standards and the vocabular terms in the standards will help ou know eactl what ou are epected to learn in this module. 8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. What It Means to You You will use an algebraic representation to describe a dilation. EXMPLE 8.G.3 The blue square D is the preimage. Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. The coordinates of the vertices of the original image are multiplied b for the green square. Green square: (, ) (, ) D' - D - ' ' ' The coordinates of the vertices of the original image are multiplied b 1_ for the purple square. Purple square: (, ) ( 1_, 1_ ) 8.G. Understand that a twodimensional figure is similar to another if the second can be obtained from the first b a sequence of rotations, reflections, translations, and dilations; given two similar twodimensional figures, describe a sequence that ehibits the similarit between them. Visit m.hrw.com to see all ommon ore Standards eplained. What It Means to You You will describe a sequence of transformations between two similar figures. EXMPLE 8.G. Identif a sequence of two transformations that will transform figure into figure. Dilate with center at the origin b a scale factor of 1_. Then translate right 3 units and up units Houghton Mifflin Harcourt Publishing ompan m.hrw.com 31 Unit

5 ? LESSN 10.1 ESSENTIL QUESTIN Properties of Dilations How do ou describe the properties of dilations? 8.G. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first b a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that ehibits the similarit between them. lso 8.G.3 EXPLRE TIVITY 1 Eploring Dilations The missions that placed 1 astronauts on the moon were controlled at the Johnson Space enter in Houston. The to models at the right are scaled-down replicas of the Saturn V rocket that powered the moon flights. Each replica is a transformation called a dilation. Unlike the other transformations ou have studied translations, rotations, and reflections dilations change the size (but not the shape) of a figure. 8.G. enter of dilation R' Ever dilation has a fied point called the center of dilation located where the lines connecting corresponding parts of figures intersect. Triangle R S T is a dilation of triangle RST. Point is the center of dilation. R S T S' T' Use a ruler to measure segments _ R, _ R, _ S, _ S, _ T, and _ T to the nearest millimeter. Record the measurements and ratios in the table. R R R R S S S S T T T T Houghton Mifflin Harcourt Publishing ompan D Write a conjecture based on the ratios in the table. Measure and record the corresponding side lengths of the triangles. R S RS R S RS S T ST S T ST Write a conjecture based on the ratios in the table. R T RT R T RT E Measure the corresponding angles and describe our results. Lesson

6 EXPLRE TIVITY 1 (cont d) Reflect 1. Two figures that have the same shape but different sizes are called similar. re triangles RST and R S T similar? Wh or wh not?. ompare the orientation of a figure with the orientation of its dilation. EXPLRE TIVITY 8.G.3 Eploring Dilations on a oordinate Plane In this activit ou will eplore how the coordinates of a figure on a coordinate plane are affected b a dilation. omplete the table. Record the - and -coordinates of the points in the two figures and the ratios of the -coordinates and the -coordinates. - ' D' ' ' D - Verte Verte D D Ratio of -coordinates ( D D) Ratio of -coordinates ( D D) Houghton Mifflin Harcourt Publishing ompan Write a conjecture about the ratios of the coordinates of a dilation image to the coordinates of the original figure. 318 Unit

7 Reflect 3. In Eplore ctivit 1, triangle R S T was larger than triangle RST. How is the relationship between quadrilateral D and quadrilateral D different? Math Talk Mathematical Practices How are dilations different from the other transformations ou have learned about? Finding a Scale Factor s ou have seen in the two activities, a dilation can produce a larger figure (an enlargement) or a smaller figure (a reduction). The scale factor describes how much the figure is enlarged or reduced. The scale factor is the ratio of a length of the image to the corresponding length on the original figure. In Eplore ctivit 1, the side lengths of triangle R S T were twice the length of those of triangle RST, so the scale factor was. In Eplore ctivit, the side lengths of quadrilateral D were half those of quadrilateral D, so the scale factor was 0.5. Math n the Spot m.hrw.com EXMPLE 1 8.G. Houghton Mifflin Harcourt Publishing ompan n art suppl store sells several sizes of drawing triangles. ll are dilations of a single basic triangle. The basic triangle and one of its dilations are shown on the grid. Find the scale factor of the dilation. STEP 1 STEP Use the coordinates to find the lengths of the sides of each triangle. Triangle : = = 3 Triangle : = = Find the ratios of the corresponding sides. = _ = = _ 3 = The scale factor of the dilation is ' ' ' 8 10 Since the scale factor is the same for all corresponding sides, ou can record just two pairs of side lengths. Use one pair as a check on the other. Reflect. Is the dilation an enlargement or a reduction? How can ou tell? Lesson

8 YUR TURN Personal Math Trainer nline Practice and Help m.hrw.com Math Talk Mathematical Practices Which scale factors lead to enlargements? Which scale factors lead to reductions? 5. Find the scale factor of the dilation D D' G G' E E' F F' 8 10 Guided Practice Use triangles and for 1 5. (Eplore ctivities 1 and, Eample 1) 1. For each pair of corresponding vertices, find the ratio of the -coordinates and the ratio of the -coordinates. ratio of -coordinates = ratio of -coordinates =. I know that triangle is a dilation of triangle because the ratios of the corresponding -5 ' 5 ' 5 -coordinates are and the ratios of the corresponding -coordinates are. ' The ratio of the lengths of the corresponding sides of triangle and triangle equals.?. The corresponding angles of triangle and triangle are. 5. The scale factor of the dilation is. ESSENTIL QUESTIN HEK-IN. How can ou find the scale factor of a dilation? Houghton Mifflin Harcourt Publishing ompan 30 Unit

9 Name lass Date 10.1 Independent Practice 8.G.3, 8.G. m.hrw.com Personal Math Trainer nline Practice and Help For 7 11, tell whether one figure is a dilation of the other or not. Eplain our reasoning. 10. Quadrilateral MNPQ is the same shape but a different size than quadrilateral M N P Q. 7. Quadrilateral MNPQ has side lengths of 15 mm, mm, 1 mm, and 18 mm. Quadrilateral M N P Q has side lengths of 5 mm, 8 mm, 7 mm, and mm. 8. Triangle RST has angles measuring 38 and 75. Triangle R S T has angles measuring 7 and 38. The sides are proportional. 11. n a coordinate plane, triangle UVW has coordinates U(0, 1), V(8, ), and W(, -). Triangle U V W has coordinates U (15, 9), V (,.5), and W ( 18, -3). 9. Two triangles, Triangle 1 and Triangle, are similar. Houghton Mifflin Harcourt Publishing ompan omplete the table b writing same or changed to compare the image with the original figure in the given transformation. 1. Translation 13. Reflection Image ompared to riginal Figure rientation Size Shape 1. Rotation 15. Dilation 1. Describe the image of a dilation with a scale factor of 1. Lesson

10 Identif the scale factor used in each dilation ' ' -5 5 D D' ' -5 8 ' ' ' 8 FUS N HIGHER RDER THINKING Work rea 19. ritical Thinking Eplain how ou can find the center of dilation of a triangle and its dilation. 0. Make a onjecture a. square on the coordinate plane has vertices at (, ), (, ), (, ), and (, ). dilation of the square has vertices at (, ), (, ), (, ), and (, ). Find the scale factor and the perimeter of each square. b. square on the coordinate plane has vertices at ( 3, 3), (3, 3), (3, 3), and ( 3, 3). dilation of the square has vertices at (, ), (, ), (, ), and (, ). Find the scale factor and the perimeter of each square. c. Make a conjecture about the relationship of the scale factor to the perimeter of a square and its image. Houghton Mifflin Harcourt Publishing ompan 3 Unit

11 ? LESSN 10. lgebraic Representations of Dilations ESSENTIL QUESTIN 8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. How can ou describe the effect of a dilation on coordinates using an algebraic representation? EXPLRE TIVITY 1 8.G.3 Graphing Enlargements When a dilation in the coordinate plane has the origin as the center of dilation, ou can find points on the dilated image b multipling the - and -coordinates of the original figure b the scale factor. For scale factor k, the algebraic representation of the dilation is (, ) (k, k). For enlargements, k > 1. The figure shown on the grid is the preimage. The center of dilation is the origin. List the coordinates of the vertices of the preimage in the first column of the table. Preimage (, ) Image (3, 3) 7 (, ) (, ) -7 7 Houghton Mifflin Harcourt Publishing ompan D What is the scale factor for the dilation? ppl the dilation to the preimage and write the coordinates of the vertices of the image in the second column of the table. Sketch the image after the dilation on the coordinate grid. -7 Math Talk Mathematical Practices What effect would the dilation (, ) (, ) have on the radius of a circle? Lesson

12 EXPLRE TIVITY 1 (cont d) Reflect 1. How does the dilation affect the length of line segments?. How does the dilation affect angle measures? EXPLRE TIVITY 8.G.3 Graphing Reductions For scale factors between 0 and 1, the image is smaller than the preimage. This is called a reduction. The arrow shown is the preimage. The center of dilation is the origin. List the coordinates of the vertices of the preimage in the first column of the table. Preimage (, ) Image 1_ 1_ (, ) 5 What is the scale factor for the dilation? - D ppl the dilation to the preimage and write the coordinates of the vertices of the image in the second column of the table. Sketch the image after the dilation on the coordinate grid. Reflect 3. How does the dilation affect the length of line segments? -5 Houghton Mifflin Harcourt Publishing ompan. How would a dilation with scale factor 1 affect the preimage? 3 Unit

13 enter of Dilation utside the Image The center of dilation can be inside or outside the original image and the dilated image. The center of dilation can be anwhere on the coordinate plane as long as the lines that connect each pair of corresponding vertices between the original and dilated image intersect at the center of dilation. Math n the Spot m.hrw.com EXMPLE 1 8.G.3 Graph the image of after a dilation with the origin as its center and a scale factor of 3. What are the vertices of the image? STEP 1 Multipl each coordinate of the vertices of b 3 to find the vertices of the dilated image. 8 (, ) (3, 3) (1, 1) (1 3, 1 3) (3, 3) (3, 1) (3 3, 1 3) (9, 3) (1, 3) (1 3, 3 3) (3, 9) The vertices of the dilated image are (3, 3), (9, 3), and (3, 9). 8 STEP Graph the dilated image. 8 ' ' ' Math Talk Mathematical Practices Describe how ou can check graphicall that ou have drawn the image triangle correctl. Houghton Mifflin Harcourt Publishing ompan YUR TURN 8 5. Graph the image of XYZ after a dilation with a scale factor of 1_ and the origin as 3 its center. Then write an algebraic rule to describe the dilation. 8 Z X 8 Y Personal Math Trainer nline Practice and Help m.hrw.com Lesson

14 Guided Practice 1. The grid shows a diamond-shaped preimage. Write the coordinates of the vertices of the preimage in the first column of the table. Then appl the dilation (, ) ( 3 _, 3 _ ) and write the coordinates of the vertices of the image in the second column. Sketch the image of the figure after the dilation. (Eplore ctivities 1 and ) Preimage Image (, 0) (3, 0) Graph the image of each figure after a dilation with the origin as its center and the given scale factor. Then write an algebraic rule to describe the dilation. (Eample 1). scale factor of scale factor of 1_ I H F G 8 8? ESSENTIL QUESTIN HEK-IN. dilation of (, ) (k, k) when 0 < k < 1 has what effect on the figure? What is the effect on the figure when k > 1? Houghton Mifflin Harcourt Publishing ompan 3 Unit

15 Name lass Date 10. Independent Practice 8.G.3 5. The blue square is the preimage. Write two algebraic representations, one for the dilation to the green square and one for the dilation to the purple square. ' m.hrw.com Personal Math Trainer nline Practice and Help 9. Represent Real-World Problems The blueprints for a new house are scaled so that 1_ inch equals 1 foot. The blueprint is the preimage and the house is the dilated image. The blueprints are plotted on a coordinate plane. a. What is the scale factor in terms of inches to inches? - D' D ' b. ne inch on the blueprint represents how man inches in the actual house? How man feet? ' - c. Write the algebraic representation of the dilation from the blueprint to the house.. ritical Thinking triangle has vertices (-5, -), (, ), and (, -3). The center of dilation is the origin and (, ) (3, 3). What are the vertices of the dilated image? d. rectangular room has coordinates Q(, ), R(7, ), S(7, 5), and T(, 5) on the blueprint. The homeowner wants this room to be 5% larger. What are the coordinates of the new room? Houghton Mifflin Harcourt Publishing ompan 7. ritical Thinking M N P has vertices at M (3, ), N (, ), (, 7), and P (3, 7). The center of dilation is the origin. MNP has vertices at M(.5, ), N(9, ), (9, 10.5), and P (.5, 10.5). What is the algebraic representation of this dilation? e. What are the dimensions of the new room, in inches, on the blueprint? What will the dimensions of the new room be, in feet, in the new house? 8. ritical Thinking dilation with center (0,0) and scale factor k is applied to a polgon. What dilation can ou appl to the image to return it to the original preimage? Lesson

16 10. Write the algebraic representation of the dilation shown FUS N HIGHER RDER THINKING Work rea 11. ritique Reasoning The set for a school pla needs a replica of a historic building painted on a backdrop that is 0 feet long and 1 feet high. The actual building measures 00 feet long and 30 feet high. stage crewmember writes (, ) ( 1 to represent the dilation. Is the 1, 1 1 ) crewmember s calculation correct if the painted replica is to cover the entire backdrop? Eplain. 1. ommunicate Mathematical Ideas Eplain what each of these algebraic transformations does to a figure. a. (, ) (, -) b. (, ) (-, -) c. (, ) (, ) d. (, ) ( _ 3, ) e. (, ) (0.5, 1.5) 13. ommunicate Mathematical Ideas Triangle has coordinates (1, 5), (-, 1), and (-, ). Sketch triangle and for the dilation (, ) (-, -). What is the effect of a negative scale factor? Houghton Mifflin Harcourt Publishing ompan 38 Unit

17 ? LESSN 10.3 Similar Figures ESSENTIL QUESTIN 8.G. Understand that a two-dimensional figure is similar to another if the second can be obtained from the first b a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that ehibits the similarit between them. What is the connection between transformations and the orientations of similar figures? EXPLRE TIVITY 8.G. ombining Transformations with Dilations When creating an animation, figures need to be translated, reflected, rotated, and sometimes dilated. s an eample of this, appl the indicated sequence of transformations to the rectangle. Each transformation is applied to the image of the previous transformation, not to the original figure. Label each image with the letter of the transformation applied. (, ) ( + 7, - ) 7 (, ) (, -) rotation 90 clockwise around the origin D E F G (, ) ( + 5, + 3) (, ) (3, 3) List the coordinates of the vertices of rectangle E. ompare the following attributes of rectangle E to those of the original figure. Shape Size ngle Measures Lesson

18 EXPLRE TIVITY (cont d) Reflect 1. Which transformation represents the dilation? How can ou tell?. sequence of transformations containing a single dilation is applied to a figure. re the original figure and its final image congruent? Eplain. Math n the Spot m.hrw.com Similar Figures Two figures are similar if one can be obtained from the other b a sequence of translations, reflections, rotations, and dilations. Similar figures have the same shape but ma be different sizes. When ou are told that two figures are similar, there must be a sequence of translations, reflections, rotations, and/or dilations that can transform one to the other. EXMPLE 1 8.G. M Notes Identif a sequence of transformations that will transform figure into figure. Tell whether the figures are congruent. Tell whether the are similar Unit oth figures are squares whose orientations are the same, so no reflection or rotation is needed. Figure has sides twice as long as figure, so a dilation with a scale factor of is needed. Figure is moved to the right and above figure, so a translation is needed. sequence of transformations that will accomplish this is a dilation b a scale factor of centered at the origin followed b the translation (, ) ( +, + ). The figures are not congruent, but the are similar. Houghton Mifflin Harcourt Publishing ompan

19 Identif a sequence of transformations that will transform figure into figure D. Include a reflection. Tell whether the figures are congruent. Tell whether the are similar. 8 D - The orientation of figure D is reversed from that of figure, so a reflection over the -ais is needed. Figure D has sides that are half as long as figure, so a dilation with a scale factor of 1 _ is needed. Figure D is moved above figure, so a translation is needed. sequence of transformations that will accomplish this is a dilation b a scale factor of 1 _ centered at the origin, followed b the reflection (, ) (-, ), followed b the translation (, ) (, + 5). The figures are not congruent, but the are similar. Identif a sequence of transformations that will transform figure into figure D. Include a rotation. Math Talk Mathematical Practices figure and its image have different sizes and orientations. What do ou know about the sequence of transformations that generated the image? The orientation of figure D is reversed from that of figure, so a rotation of 180º is needed. Figure D has sides that are half as long as figure, so a dilation with a scale factor of 1 _ is needed. Figure D is moved above figure, so a translation is needed. sequence of transformations that will accomplish this is a rotation of 180º about the origin, followed b a dilation b a scale factor of 1 _ centered at the origin, followed b the translation (, ) (, + 5). Houghton Mifflin Harcourt Publishing ompan YUR TURN 3. Look again at the Eplore ctivit. Start with the original figure. reate a new sequence of transformations that will ield figure E, the final image. Your transformations do not need to produce the images in the same order in which the originall appeared. Personal Math Trainer nline Practice and Help m.hrw.com Lesson

20 Guided Practice 1. ppl the indicated sequence of transformations to the square. ppl each transformation to the image of the previous transformation. Label each image with the letter of the transformation applied. (Eplore ctivit) 8 (, ) (-, ) Rotate the square 180 around the origin. (, ) ( - 5, - ) D (, ) ( 1_, 1_ ) Identif a sequence of two transformations that will transform figure into the given figure. (Eample 1). figure 8 D 3. figure ?. figure D ESSENTIL QUESTIN HEK-IN 5. If two figures are similar but not congruent, what do ou know about the sequence of transformations used to create one from the other? - -8 Houghton Mifflin Harcourt Publishing ompan 33 Unit

21 Name lass Date 10.3 Independent Practice 8.G. m.hrw.com Personal Math Trainer nline Practice and Help. designer creates a drawing of a triangular sign on centimeter grid paper for a new business. The drawing has sides measuring cm, 8 cm, and 10 cm, and angles measuring 37, 53, and 90. To create the actual sign shown, the drawing must be dilated using a scale factor of 0. a. Find the lengths of the sides of the actual sign. b. Find the angle measures of the actual sign. Jan s afé c. The drawing has the hpotenuse on the bottom. The business owner would like it on the top. Describe two transformations that will do this. d. The shorter leg of the drawing is currentl on the left. The business owner wants it to remain on the left after the hpotenuse goes to the top. Which transformation in part c will accomplish this? In Eercises 7 10, the transformation of a figure into its image is described. Describe the transformations that will transform the image back into the original figure. Then write them algebraicall. 7. The figure is reflected across the -ais and dilated b a scale factor of 3. Houghton Mifflin Harcourt Publishing ompan 8. The figure is dilated b a scale factor of 0.5 and translated units left and 3 units up. 9. The figure is dilated b a scale factor of 5 and rotated 90 clockwise. Lesson

22 10. The figure is reflected across the -ais and dilated b a scale factor of. FUS N HIGHER RDER THINKING Work rea 11. Draw onclusions figure undergoes a sequence of transformations that include dilations. The figure and its final image are congruent. Eplain how this can happen. 1. Multistep graphic artist is using transformations to sketch ideas for a logo design. Start with the image provided and label each transformation with the letter of the sequence that is applied. ppl each sequence of transformations to the previous image.. (, ) ( 1_, 1_ ) with the center at the origin, (, ) (, - 1) (, ) ( -, + 1), (, ) (, -). 13. Justif Reasoning In Eercise 1, the sketch was dilated b a scale factor of 1_ and translated down 1 unit. Is this the same as translating the sketch down 1 unit and then dilating b a scale factor of 1_? Eplain how the two results are related. Houghton Mifflin Harcourt Publishing ompan 33 Unit

23 MDULE QUIZ Read 10.1 Properties of Dilations Determine whether one figure is a dilation of the other. Justif our answer. Personal Math Trainer nline Practice and Help m.hrw.com 1. Triangle XYZ has angles measuring 5 and 9. Triangle X Y Z has angles measuring 9 and 9.. Quadrilateral DEFG has sides measuring 1 m, 8 m, m, and 0 m. Quadrilateral D E F G has sides measuring 0 m, 35 m, 30 m, and 5 m. 10. lgebraic Representations of Dilations Dilate each figure with the origin as the center of dilation. 3. (, ) (0.8, 0.8). (, ) (.5,.5) Similar Figures Houghton Mifflin Harcourt Publishing ompan 5. Describe what happens to a figure when the given sequence of transformations is applied to it: (, ) (-, ); (, ) (0.5, 0.5); (, ) ( -, + ) ESSENTIL QUESTIN. How can ou use dilations to solve real-world problems? Module

24 MDULE 10 MIXED REVIEW ssessment Readiness m.hrw.com Personal Math Trainer nline Practice and Help 1. Triangle is dilated b a scale factor of with the origin as its center and then reflected across the -ais. Look at each ordered pair. Is the ordered pair a verte of the image? Select Yes or No for ordered pairs.. (-, 10) Yes No. (-, ) Yes No. (10, -) Yes No. hoose True or False for each statement.. No integers are irrational numbers. True False. No real numbers are rational numbers. True False. ll integers are whole numbers. True False D. ll whole numbers are integers. True False In a video game, a rectangular map has vertices M(10, 10), N(10, 0), P(0, 0), and Q(0, 10). When a plaer clicks the map, it is enlarged b a scale factor of.5 with the origin as the center of dilation. What are the coordinates of the vertices of the enlarged map? Describe the algebraic rule ou used to find the coordinates.. n engineer is working on the design of a bridge. He draws the two triangles shown. Is triangle similar to triangle? Use a sequence of transformations to eplain how ou know. - - (, 1.5) (, -1.5) Houghton Mifflin Harcourt Publishing ompan 33 Unit