Name. JEFFERSON PARISH Math / Grade 8 / Transformations review. Teacher Period

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1 JEFFERSON PARISH Math / Grade 8 / Transformations review 1. Roman is writing a program for a new computer game. He needs figure A to move to figure B. What transformation must he program into the game to make this move? Name Teacher Period Use the graph below to answer question 2. A. reflection about the x-axis B. reflection about the y-axis C. rotation 90 clockwise D. translation (x, y) (x, y 2) 2. Which triangle is a translation of triangle 2 by the rule (x, y) (x + 6, y + 0)? A. triangle 5 B. triangle 6 C. triangle 7 D. triangle 8 1

2 3. A residential construction company laid the foundation for a new house at the corner of Park Street and Second Avenue. Right trapezoid HOME shows the location of the foundation in the diagram below. Use the information below to answer questions 4 and 5. Walt has an octagonal carpet near the corner of his living room, as shown on the coordinate plane below. 4. If Walt translates the carpet according to the rule (x, y) (x 2, y 2), how will its angle measures be affected? The company plans to lay another foundation, H O M E, across Park Street so that it is a reflection of HOME. Which of the following will be true if the foundation for H O M E is laid? A. H will be a right angle. B. O will be an obtuse angle. C. M will be a straight angle. D. E will be an acute angle. A. They will be halved. B. They will be doubled. C. They will be the same. D. They will be decreased by If Walt translates the carpet according to the rule (x, y) (x 2, y 2), how will its sides be affected? A. The longer sides will remain parallel. B. The shorter sides will remain perpendicular. C. The horizontal and vertical sides will become longer. D. The horizontal and vertical sides will become shorter. 2

6. The equations below show the equations for two different lines. y = 1 5 x 4 y = 1 5 x + 4 7. The shaded figure on the coordinate plane below represents the former location of a baseball park.

3 6. The equations below show the equations for two different lines. y = 1 5 x 4 y = 1 5 x The shaded figure on the coordinate plane below represents the former location of a baseball park. Rotating the old location 180 about the origin shows the location of the new park that replaced it. If both lines are rotated 90 counterclockwise about the origin to form two new lines, which of the following correctly describes the relationship between the two new lines? A. collinear B. parallel C. perpendicular D. skew Which term best describes the relationship between the old park and the new park? A. congruent B. parallel C. perpendicular D. similar 3

4 8. The white figure on the coordinate plane below represents where Ron parked his truck yesterday. The shaded figure shows where he parked it today. 9. Use the graph below to solve the problem. Which sequence correctly describes the transformation from ABCD to A B C D? Which of the following does not describe a possible transformation between the two figures? A. dilation B. reflection C. rotation D. translation A. Translate (x, y) (x + 10, y + 1). Reflect over the x-axis. B. Translate (x, y) (x 1, y + 1). Rotate 180 about the origin. C. Translate (x, y) (x + 1, y 1). Reflect over the x-axis and y-axis. D. Translate (x, y) (x 1, y 6). Rotate 90 counterclockwise about the origin. 4

5 10. The coordinates of a triangle are (3, 1), (7, 2), and (1, 4). What are the coordinates of the image of this triangle after the transformation up 2, left 6? 11. Δ ABC has vertices A ( 2, 3), B (4,1), and C (2, 3). What are the coordinates of its image ΔA'B'C' after reflecting it over the x- axis? A. ( 6, 2), ( 8, 1), ( 2, 1) B. ( 3, 1), (1, 0), ( 5, 2) C. ( 1, 2), (1, 5), (5, 4) D. (1, 3), (0, 1), ( 2, 5) A. A'( 2, 3), B'(4, 1), C'(2, 3) B. A'(2, 3), B'( 4, 1), C'( 2, 3) C. A'(2, 3), B'( 4, 1), C'( 2, 3) D. A'( 2, 3), B'(4, 1), C'(2, 3) 5

6 12. Lily transformed ABC below. The result is shown in dotted lines. Which of the following describes Lily's transformation? Use the graph below to answer question How was ABCD transformed to A B C D? A. rotated 90 clockwise about the origin B. rotated 90 counterclockwise about the origin C. rotated 180 about the origin D. reflected across the x-axis A. Reflect over the x-axis and dilate by a scale factor of 2 relative to (0, 0). B. Reflect over the x-axis and dilate by a scale factor of 1 2 relative to (0, 0). C. Rotate 90 counterclockwise and dilate by a scale factor of 2 relative to (0, 0). D. Rotate 90 counterclockwise and dilate by a scale factor of 1 2 relative to (0, 0). 6

7 Use the information below to answer question 14. A thought bubble from a comic strip is drawn on the coordinate plane below. 15. Jonesboro Police Department is considering re-routing traffic at the intersections shown below where more than the average number of accidents are reported. What is the geometric description of the relationship between Ә A and Ә B? 14. Which transformation can be used to turn figure A into figure B? A. Dilate by a factor of 3 relative to the origin. Translate 1 unit to the left. B. Dilate by a factor of 3 relative to the origin. Translate 1 unit to the right. C. Dilate by a factor of 1 3 relative to the origin. Translate 1 unit to the left. A. alternate exterior angles B. alternate interior angles C. corresponding angles D. linear pair D. Dilate by a factor of 1 3 relative to the origin. Translate 1 unit to the right. 7

8 16. Below is a map of Miles neighborhood. The avenues are parallel, and Miles walks on a path across them to get to the park. If Ә 3 is 50, what is the measure of Ә 4? 18. Given that r s and t is a transversal, which of the following lists shows all angles that are congruent to Ә 1? A. 40 B. 50 C. 130 D. 150 A. Ә 1 ӽ Ә 3 B. Ә 1 ӽ Ә 3, Ә 1 ӽ Ә 5 C. Ә 1 ӽ Ә 3, Ә 1 ӽ Ә 5, Ә 1 ӽ Ә 7 D. Ә 1 ӽ Ә 3, Ә 1 ӽ Ә Suppose two parallel lines are cut by a transversal and angles 1 and 5 are alternate exterior angles. If m Ә 5 = 84, what is m Ә 1? A. m Ә 1 = 6 B. m Ә 1 = 84 C. m Ә 1 = 96 D. m Ә 1 = 174 8

9 19. Alan laid a wooden board across a small stream in order to cross it. The diagram below shows the board, the stream, and the distance between the stream s banks where the board intersects the banks. 20. Line segment AC and line segment ED are parallel. Which statement could be used to argue that ABC and EBD are similar? A. BC and AB are equal. B. DB + DC = CB C. ә 1 = ә 3, ә 2 = ә 4 Which of the following would be sufficient to prove that triangle BGH is similar to triangle JDC? D. ә 1 = ә 2, ә 3 = ә 4 A. AE ӝ FK B. BH ӝ CJ C. ә ABG ӽ ә DJK D. ә GBH ӽ ә DJC 9

10 JEFFERSON PARISH Open-Response / Grade 8 / Transformations review Name Teacher Period MATH OPEN-RESPONSE ITEM A A. Randa is designing a stained-glass window. The grid provided in your Student Answer Document shows Randa's first design, labeled F1. 1. Rotate F1 clockwise 90 about point D, resulting in Figure 2. Label each vertex with its corresponding letter. Label this figure F2. 2. Reflect F2 over the x-axis, resulting in Figure 3. Label each vertex with its corresponding letter. Label this figure F3. 3. Translate F3 to the right 8 units and up 11 units, resulting in Figure 4. Label each vertex with its corresponding letter. Label this figure F4. 10

11 JEFFERSON PARISH Student Answer Document / Grade 8 / Transformations review Name Teacher Period A 11

12 MATH OPEN-RESPONSE ITEM A (8.G.1A, 8.G.1B, 8.G.1C) A. Randa is designing a stained-glass window. The grid provided in your Student Answer Document shows Randa's first design, labeled F1. 1. Rotate F1 clockwise 90 about point D, resulting in Figure 2. Label each vertex with its corresponding letter. Label this figure F2. 2. Reflect F2 over the x-axis, resulting in Figure 3. Label each vertex with its corresponding letter. Label this figure F3. 3. Translate F3 to the right 8 units and up 11 units, resulting in Figure 4. Label each vertex with its corresponding letter. Label this figure F4. RUBRIC FOR MATH OPEN-RESPONSE ITEM A (8.G.1A, 8.G.1B, 8.G.1C) Score Description 4 The student earns 6 points. The response contains no incorrect work. 3 The student earns 4 5 points. 2 The student earns 2 3 points. 1 The student earns 1 point or some minimal understanding is shown. 0 The student earns 0 points. No understanding is shown. B Blank No Response. (No attempt to answer the item. Score of 0 assigned for the item.)

Solution and Scoring Part Points 1 2 points possible 1 point: Student correctly drew Figure 2. AND 1 point: Student correctly labeled Figure 2.

13 Solution and Scoring Part Points 1 2 points possible 1 point: Student correctly drew Figure 2. AND 1 point: Student correctly labeled Figure points possible (Based on student's answer from Part 1.) 1 point: Student correctly drew Figure 3. AND 1 point: Student correctly labeled Figure points possible (Based on student's answer from Part 2.) 1 point: Student correctly drew Figure 4. AND 1 point: Student correctly labeled Figure 4. Give credit for the following or equivalent graph. Note: Hash marks are not required on F2, F3, or F4 to earn a score of 6.

14 JEFFERSON PARISH Math / Grade 8 / Transformations review Answer Key and Alignment Answer Source SLE CC-Standard 1. A TLI G.9.8.2b 8.G.1a 2. B TLI G.9.8.2a 8.G.1a 3. D TLI 8.G.1b 4. C TLI 8.G.1b 5. A TLI 8.G.1c 6. B TLI 8.G.1c 7. A TLI 8.G.2 8. A TLI 8.G.2 9. B TLI 8.G B TLI G.9.8.2a 8.G A TLI G.9.8.2b 8.G B TLI G.9.8.2c 8.G C TLI 8.G C TLI 8.G B TLI G.8.7.3c 8.G.5(A) 16. C TLI G.8.7.3c 8.G.5(A) 17. B TLI G.8.7.3c 8.G.5(B) 18. C TLI G.8.7.3c 8.G.5(B) 19. D TLI 8.G.5(C) 20. D TLI 8.G.5(C)

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