Original site. translation. transformation. Decide whether the red figure is a translation of the blue figure. Compare a Figure and Its Image

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1 Page of Translations Goal Identif and use translations. Ke Words translation image transformation In 996, New York Cit s Empire Theater was slid 70 feet up 2nd Street to a new location. Original site A slide is also called a translation. The new figure after the translation is the image. In this book, the original figure is given in blue and its image in red, as shown at the right. Translation Image A translation is one kind of transformation. A transformation is an operation that maps, or moves, a figure onto an image. You will stud other transformations in Lessons 5.7, 7.6, and.8. Student Help VOCAULARY TIP Use the following relationship to help ou remember that a translation is a slide: translation slide EXAMPLE Compare a Figure and Its Image Decide whether the red figure is a translation of the blue figure. a. b. c. Solution a. Yes, this is a translation. b. No, this is not a translation. The image is a mirror image of the original figure. c. No, this is not a translation. The original figure is rotated. Compare a Figure and Its Image Decide whether the red figure is a translation of the blue figure Chapter 3 Parallel and Perpendicular Lines

2 Page 2 of 8 Student Help READING TIP In the diagram at the right, A is read as A prime. Labeling Translations When labeling points on the image, write the prime smbol ( ) net to the letter used in the original figure, as shown at the right. A In a translation, segments connecting points Image in the original figure to their corresponding points in the image are congruent and parallel. For eample, AA &** and &* at the right are congruent and parallel. A EXAMPLE 2 Describe Translations Describe the translation of the segment. Solution Point P is moved units to the right and 2 units down to get to point P. So, ever point on PQ &* moves units to the right and 2 units down. P(2, ) Œ(, 2) 2 P (6, 2) Œ (5, 0) Translations in a coordinate plane can also be described using the following coordinate notation: (, ) ( a, b) Each point shifts a units horizontall (right or left) and b units verticall (up or down). When moving right or up, add the number of units. When moving left or down, subtract the number of units. Here are some eamples: (, ) (, ) (, ) (, ) IStudent Help I C L A S S Z O N E. C O M MORE EXAMPLES More eamples at classzone.com EXAMPLE Describe the translation using coordinate notation. Solution 3 Use Coordinate Notation Each point is moved 3 units to the left and units up. ANSWER The translation can be described using the notation (, ) ( 3, ) Translations 53

3 Page 3 of 8 Describe Translations Describe the translation using words and coordinate notation EXAMPLE Draw Translated Figures Student Help Draw the triangle given b points A( 2, 5), (0, 7), and C(3, 7). Then draw the image of the triangle after the translation given b (, ) ( 2, 3). READING TIP In this book, shapes are named b listing in order the labels at their corners. For eample, the blue triangle in Eample is named T AC. Solution First, sketch T AC as shown. To find points A,, and C, start at points A,, and C, and slide each point 2 units to the right and 3 units down. T AC T A C A 2 C 3 C A( 2, 5) A (0, 2) (0, 7) (2, ) C(3, 7) C (5, ) A Notice that each -value of T A C is 2 units more than the corresponding -value of T AC and each -value of T A C is 3 units less than the corresponding -value of T AC. Draw Translated Figures Draw the image of the figure after the given translation. 6. (, ) ( 3, 2) 7. (, ) ( 3, ) F G J H W X Z Y 5 Chapter 3 Parallel and Perpendicular Lines

4 Page of Eercises Guided Practice Vocabular Check. What is a translation? 2. Complete the statement: A translation shows a blue triangle and a red triangle. The blue triangle is the original figure and the red triangle is the?. Skill Check Window Frames Decide whether opening the window is a translation of the moving part. 3. Double hung. Casement 5. Sliding Decide whether the statement is true or false. Eplain. 6. The red figure is a translation of the blue figure. 7. To move from T AC to T A C, shift 3 units to the right and 2 units up. 8. The translation from T AC to T A C is given b (, ) ( 3, 2). C A C A Practice and Applications Etra Practice See p Compare a Figure and Its Image Decide whether the red figure is a translation of the blue figure Homework Help Eample : Es. 9 Eample 2: Es. 5 2 Eample 3: Es. 22, 23 Eample : Es Translations 55

5 Page 5 of 8 Matching Translations Match the description of the translation with its diagram. 5. units right and 3 units up 6. 6 units right and 2 units down 7. 7 units left and unit up 8. 5 units right and 2 units down A.. C. D. Describing Translations Describe the translation using words Coordinate Notation Describe the translation using coordinate notation A Point and Its Image Find the image of the point using the translation (, ) (, 3). 2. (2, 5) 25. ( 3, 7) 26. (, ) 27. (, 6) 28. (0, 0) 29. (, 3) 30. (3, ) 3. (, ) 56 Chapter 3 Parallel and Perpendicular Lines

6 Page 6 of 8 Finding an Image Find the coordinates of P, Q, R, and S using the given translation. 32. (, ) (, ) Π33. (, ) ( 3, 2) 3 R 3. (, ) ( 5, 5) P Chess CHESS TEAMS The chess team at the Universit of Marland, altimore Count (UMC), has become a strong, nationall recognized team. This is due in part to the efforts of UMC President Dr. Freeman A. Hrabowski, III (second from the left). 35. (, ) (, 3) Chess In chess, si different kinds of pieces are moved according to individual rules. The board below shows some moves for the Knight (the piece shaped like a horse). 36. Describe the translation used b the White Knight to capture the lack Pawn. 37. Assume that the White Knight has taken the place of the lack Pawn. Describe the translation used b the lack Knight to move to capture the White Knight at its new location. Drawing Translated Figures Draw the image of the figure after the given translation. 38. (, ) ( 2, ) 39. (, ) (, 5) F S E. 37 E. 36 A C H G 0. (, ) ( 5, 3). (, ) ( 3, 8) Q P W 2 X S R Z Y Use Points on an Image A point on an image and the translation are given. Find the corresponding point on the original figure. 2. Point on image: (0, 3); translation: (, ) ( 3, 2) 3. Point on image: ( 2, ); translation: (, ) ( 5, ). Point on image: (6, ); translation: (, ) ( 3, 7) 3.7 Translations 57

7 Page 7 of 8 You be the Judge 5. The figure on the grid shown at the right is the image after the translation (, ) ( 6, ). One of our classmates tells ou that C on the original figure is (2, 2). Do ou agree? Eplain our reasoning. C A Technolog In Eercises 6 and 7, use geometr software to complete the steps below. Draw a triangle and translate it. 2 Construct &* JJ and KK &**. 6. If two lines have the same slope, then the are parallel. Measure the slopes of &* JJ and KK &**. Are&* JJ and KK &** parallel? 7. What should makjj mak KJ be? Measure the angles and check our answer. J K L J K L Standardized Test Practice Mied Review 8. Challenge Point C is located at (, 3). The translation that shifts C to C is given b (, ) ( 5, ). The translation that shifts C to C is given b (, ) (, 8). Give the coordinate notation that describes the translation directl from C to C. (Hint: Start b plotting C, C, and C.) Multiple Choice In Eercises 9 and 50, use the diagram below. 9. Find the coordinates of T using the translation (, ) ( 5, 2). A (3, 7) (0, 0) C (3, 5) D ( 5, 7) 50. Find the coordinates of W using the translation (, ) ( 3, 3). F (5, ) G (, 7) H (5, 7) J (, ) Classifing Angles State whether the angle appears to be acute, right, obtuse, or straight. Then estimate its measure. (Lesson.6) W V T U A C F G H Y X Z 58 Chapter 3 Parallel and Perpendicular Lines

8 Page 8 of 8 Algebra Skills Problem Solving Use problem solving strategies to answer the question. (Skills Review, p. 653) 5. Your telephone compan charges $.5 per minute for all long distance calls. This month ou paid $2.60 for long distance calls. How man minutes did ou spend on long distance calls? 55. You just bought a CD single that has four tracks. In how man different orders can the songs be plaed? Ordering Numbers Write the numbers in order from least to greatest. (Skills Review, p. 662) , 0.5, 0,.0, 0., ,.2, 0.7,.5, 0,., , 7.6, 0.77, 6.6, 0.7, , 6.3, 6.8, 6., 6, 6.09 Quiz 3 Determine whether enough information is given to conclude that m n. Eplain. (Lesson 3.5). 2. m n 3. m n m n In Eercises 6, eplain how ou would show that p q. State an theorems or postulates that ou would use. (Lesson 3.6). p q 5. p n q 6. n q p n Draw a vertical line l and construct a line m perpendicular to it through a point P to the left of line l. (Lesson 3.6) In Eercises 8 and 9, describe the translation of the figure using coordinate notation. (Lesson 3.7) Translations 59