Unit 4 Performance Tasks

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1 ? UNIT 4 Stud Guide Review MULE 9 ESSENTIL QUESTIN Transformations and ongruence How can ou use transformations and congruence to solve real-world problems? EXMPLE Translate triangle XYZ left 4 units and down 2 units. Graph the image and label the vertices. X - Y - Z X Y Z Ke Vocabular center of rotation (centro de rotación) congruent (congruente) image (imagen) line of reflection (línea de refleión) preimage (imagen original) reflection (refleión) rotation (rotación) transformation ( transformación) translation (traslación) Translate the vertices b subtracting 4 from each -coordinate and 2 from each -coordinate. The new vertices are X (-1, 1), Y (0, ), and Z (1, -). onnect the vertices to draw triangle X Y Z.. Rotation 90 counterclockwise about the origin - -. Quadrilateral with vertices (4, 4), (, 1), (, -1) and (4, -2) is translated left 2 units and down units. Graph the preimage and the image. (Lesson 9.4) Translation 4 units right and 4 units down Triangle with vertices (1, 2), (1, 4), and (, ) is translated b (, ) ( - 4, ), and the result is reflected b (, ) (, -). Graph the preimage and the image. (Lesson 9.) - Houghton Mifflin Harcourt Publishing ompan EXERISES Perform the transformation shown. (Lessons 9.1, 9.2, 9.) 1. Reflection over the -ais 2. Translation units right Triangle RST has vertices at (-8, 2), (-4, 0), and (-12, 8). Find the vertices after the triangle has been reflected over the -ais. (Lesson 9.4) (8, 2), (4, 0), (12, 8) 8. Triangle XYZ has vertices at (, 7), (9, 14), and (12, -1). Find the vertices after the triangle has been rotated 180 about the origin. (Lesson 9.4) (-, -7), (-9, -14), (-12, 1) 9. Triangle MNP has its vertices located at (-1, -4), (-2, ), and (-, -). Find the vertices after the triangle has been reflected b (, ) (, -) and translated b (, ) ( +, ). (Lesson 9.) (, 4), (4, ), (, ) Houghton Mifflin Harcourt Publishing ompan Unit 4 Unit 4 Transformational Geometr

2 MULE 10 Transformations and Similarit MMN RE 8.G., 8.G.4 Ke oncepts dilation is a transformation that changes the position and size but not the shape of a figure. (Lesson 10.1) The scale factor of a dilation describes how much the figure is enlarged or reduced and is the ratio of a length of the image to the corresponding length of the preimage. (Lesson 10.1) To find the coordinates of a dilated image with the origin as the center, multipl the - and -coordinates of the vertices b the scale factor. (Lesson 10.2) If two figures are similar, then there eists a sequence of translations, reflections, rotations, and/or dilations that transforms one figure into the other. (Lesson 10.) Unit 4 Performance Tasks The Performance Tasks provide students with the opportunit to appl concepts from this unit in real-world problem situations. REERS IN MTH For more information about careers in mathematics as well as various mathematics appreciation topics, visit the merican Mathematical Societ at REERS IN MTH ontractor In Performance Task Item 1, students can see how a contractor uses mathematics on the job. SRING GUIES FR PERFRMNE TSKS 1. MTHEMTIL PRTIES MMN RE MP., MP.4, MP. Task Possible Points (Total: ) a b 1 point for the correct answer es, and 2 points for correctl eplaining that the area increased b a factor of, from square units to square units. 1 point for the correct answer no, and 2 points for a correct eplanation, for eample: ne side length increased b a factor of 2 and the other side length increased b a factor of. 2. MTHEMTIL PRTIES MMN RE MP., MP.4, MP.7 Possible Points (Total: ) 2 points for the correct points (0, 0), (7., 0), and (7., ) 2 points for the correct answer es, and 2 points for correctl eplaining that the angle measures are the same in both triangles, and the ratio of corresponding side lengths increase b the scale factor. 7 Unit 4

3 ? 10 MULE Transformations and Similarit Ke Vocabular center of dilation (centro de dilatación) dilation (dilatación) ESSENTIL QUESTIN enlargement How can ou use dilations, similarit, and proportionalit to solve (agrandamiento) real-world problems? reduction (reducción) scale factor (factor de escala) EXMPLE similar (semejantes) ilate triangle with the origin as the center of dilation and scale factor 1_. Graph the dilated image. 2 Multipl each coordinate of the vertices of b 1_ to find the vertices 2 of the dilated image. (, -1) - ( 1_, -1 1_ 2 2) ( 2 1_ 2, - 1_ 2) (4, ) ( 4 1_, 1_ 2 2) ( 2, -2 1_ 2) - (2, 0) ( 2 1_ 2, 0 1_ 2) (1, 0) ilate each figure with the origin as the center of the dilation. List the vertices of the dilated figure then graph the figure. (Lesson 10.2). (, ) ( 1_ 4, 1_ 4 ) 4. (, ) (2, 2) X (-2, 1); Y (-1, 1); Z (1, 2) (-2, 4); (4, 4); (, -2); (0, -2) X X Z Y Y Unit 4 Performance Tasks Z Houghton Mifflin Harcourt Publishing ompan EXERISES 1. For each pair of corresponding vertices, find the ratio of the -coordinates and the ratio of the -coordinates. (Lesson 10.1) Ratio of -coordinates: 1. 8 E E Ratio of -coordinates: 1. 4 What is the scale factor of the dilation? F -8 F 2. Rectangle WXYZ has vertices at (-2, -1), (-2, 1), (2, -1), and (2, 1). It is first dilated b (, ) (2, 2), and then translated b (, ) (, + ). (Lesson 10.) a. What are the vertices of the image? (-4, 1), (-4, ), (4, 1), (4, ) b. re the preimage and image congruent? re the similar? Eplain. The are not congruent because the lengths of the corresponding sides of the image and preimage are not equal; the are similar because the have the same shape. Unit REERS IN MTH ontractor Fernando is epanding his dog s pla ard. The original ard has a fence represented b rectangle LMN on the coordinate plane. Fernando hires a contractor to construct a new fence that should enclose times as much area as the current fence. The shape of the fence must remain the same. The contractor constructs the fence shown b rectangle L M N. L 4 L M N 2 4 a. id the contractor increase the area b the amount Fernando wanted? Eplain. Yes; the original area was 2 = square units, and the new area is = square units, and =. b. oes the new fence maintain the shape of the old fence? How do ou know? No; the corresponding side lengths are not in proportion. The ratio of the width is 2, and the ratio of the height is. 2. sail for a sailboat is represented b a triangle on the coordinate plane with vertices (0, 0), (, 0), and (, 4). The triangle is dilated b a scale factor of 1. with the origin as the center of dilation. Find the coordinates of the dilated triangle. re the triangles similar? Eplain. (0, 0), (7., 0), and (7., ); Yes; the angle measures are the same in both, and the ratio of corresponding side lengths is 1. (the scale factor). 8 Unit 4 M N Houghton Mifflin Harcourt Publishing ompan Transformational Geometr 8

4 UNIT 4 Transformational Geometr MIXE REVIEW ssessment Readiness dditional Resources m.hrw.com Personal Math Trainer nline ssessment and Intervention ssessment Resources Leveled Unit Tests:,,, Performance ssessment ssessment Readiness Tip Students can make a graph to help them understand questions for which graphs are not given. Items 2 and 8 Students can make a graph, plot the points of the original image, then perform the transformations on the figure. The can find the answer b looking at the coordinates of the vertices of the image the create. Item Students can quickl sketch a graph of a trapezoid and then translate it 8 units down. This allows them to check each statement using a concrete model of the situation. void ommon Errors Item 4 Some students will onl check the first pair of values in the table to see if the work in the equations. In this case, three of the given equations are fulfilled b the first pair of values in the table. Remind them that the need to check multiple pairs of values to make sure the table and equation match each other. Item Some students will choose answer choice because and are multiplied b coefficients less than one. Remind students that in a reduction, both variables must be multiplied b the same value. ommon ore Standards Items Grade 8 Standards Mathematical Practices 1 8.G.1 MP G. MP.2 8.G.4 MP.1 4* 8.F.4 MP.2 8.G.1 MP. 8.G. MP.2 7* 8.EE.7b MP G. MP.2 9* 8.EE.8b; 8.EE.8c MP.1 10* 8.NS.1 MP.7 11* 8.EE.8b MP G.2 MP G. MP.1 * Item integrates mied review concepts from previous modules or a previous course. 9 Unit 4

5 NT EIT--hanges must be made through "File info" orrectionke= UNIT 4 MIXE REVIEW ssessment Readiness Personal Math Trainer nline ssessment and m.hrw.com Intervention 8. rectangle has vertices (8, ), (4, ), (8, -4), and (4, -4). What are the coordinates after dilating from the origin b a scale factor of 1.? 12. triangle with vertices (-2, -), (-4, 0), and (0, 0) is congruent to a second triangle located in quadrant I with two of its vertices at (, 2) and (1, ). Houghton Mifflin Harcourt Publishing ompan Selected Response 1. What would be the orientation of the figure below after a reflection over the -ais? 2. triangle with coordinates (4, 2), (0, -), and (, ) is translated units right and rotated 180 about the origin. What are the coordinates of its image? (9, 2), (-1, -2), (, -7) (-10, ), (-1, 2), (, -) (2, -1), (-, ), (, -10) (-9, -2), (, ), (0, -). Quadrilateral LMNP has sides measuring 1, 28, 12, and 2. Which could be the side lengths of a dilation of LMNP? 24, 40, 18, 90 2, 0, 24, 20,, 1, The table below represents which equation? = + 2 = - = + = Which of the following is not true of a trapezoid that has been translated 8 units down? The new trapezoid is the same size as the original trapezoid. The new trapezoid is the same shape as the original trapezoid. The new trapezoid is in the same orientation as the original trapezoid. The -coordinates of the new trapezoid are the same as the -coordinates of the original trapezoid.. Which represents a reduction? (, ) (0.9, 0.9) (, ) (1.4, 1.4) (, ) (0.7, 0.) (, ) (2., 2.) 7. Which is the solution for 4( + 1) = 2( - 2)? = -4 = -1 = 0 = 4 (9, ), (, ), (9, -), (, -) (10, 8), (, 8), (10, ), (, ) (1, 12), (8, 12), (1, -8), (8, -8) (12, 9), (, 9), (12, -), (, -) Hot Tip! T p Make sure ou look at all answer choices before making our decision. Tr substituting each answer choice into the problem if ou are unsure of the answer. 9. Two apples plus four bananas cost $2.00. n apple costs twice as much as a banana. Using the equations 2a + 4b = 2.00 and a = 2b, where a is the cost of one apple and b is the cost of one banana, what are a and b? a = $0.2; b = $0.2 a = $0.2; b = $0.0 a = $0.0; b = $0.2 a = $0.0; b = $ Which statement is false? No integers are irrational numbers. ll whole numbers are integers. No real numbers are rational numbers. ll integers greater than or equal to 0 are whole numbers. 11. onsider the sstem of equations + 4 = 2 and 2-4 = 8. Which is its solution? = -1, = -2 = 1, = 2 = -2, = 1 = 2, = -1 a. Graph the two triangles on the same coordinate grid. (-4, 0) - (-2, -) - (1, ) (0,0) (, ) (, 2) b. What are the coordinates of the third verte of the second triangle? (, ) 1. Tamiko is planning a stone wall shaped like a triangle, with vertices at (-1, -2), (2, 2), and (-2, 2) on a coordinate grid. She plans to add a second wall, in the same shape, enclosing the first wall, with the origin as the center of dilation. The vertices of the second wall are (-, -), (, ), and (-, ). a. What scale factor did Tamiko use for the second wall? b. re the two walls similar? Eplain. Yes. Two figures are similar if one can be obtained from the other b dilation. Houghton Mifflin Harcourt Publishing ompan 40, 70, 0, 7 Unit Unit 4 8_MFLESE0718_U4SG.indd 9 2/2/1 2:12 M Transformational Geometr 40