Reflections and Translations
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- Rodger McCarthy
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1 Name: ate: 1. Parallelogram ABC was translated to parallelogram A B C. 2. Alyssa made the design shown below. How many units and in which direction were the x-coordinates of parallelogram ABC moved? A. 3 units to the right B. 3 units to the left C. 7 units to the right. 7 units to the left Which transformation could be used to show that figure A is congruent to figure B? A. add 5 to each x-coordinate B. multiply each y-coordinate by 1 C. multiply each x-coordinate by 1. rotate the figure 90 degrees about the origin page 1
2 3. Which graph shows a reflection of the rectangle across the horizontal dotted line? A. B. C.. page 2
3 4. Which of the following is a single reflection of figure N over the y-axis to form N? A. B. C.. page 3
4 5. Which figure shows the triangle below reflected over the x-axis, then reflected over the y-axis? A. B. C.. page 4
5 6. Figure EFGH in the coordinate plane has vertices at ( 5, 2), ( 5, 2), ( 1, 2), and ( 1, 2). 7. Triangle RST is shown in the coordinate plane. If the figure is translated 5 units to the right and 2 units up, what are the coordinates of the E F G H? A. (0, 4), (0, 0), (4, 0), (4, 4) B. ( 3, 7), ( 3, 3), (1, 3), (1, 7) C. ( 10, 0), ( 10, 4), ( 6, 4), ( 6, 0) What are the coordinates of R S T if the figure is reflected over the x-axis and translated down two units? A. (1, 6), (1, 9), (6, 9) B. (3, 4), (3, 7), (8, 7) C. (1, 2), (1, 5), (6, 5). (3, 2), (3, 5), (8, 5). ( 7, 3), ( 7, 7), ( 3, 7), ( 3, 3) page 5
6 8. A figure on the graph is translated down 4 units and left 2 units. Which of the following represents this single transformation? A. B. C.. page 6
7 9. Which figure is a reflection of figure P in respect to the x-axis? A. B. C.. page 7
8 10. What is the apparent image of X when triangle WXY is translated 2 units down and 5 units right? 11. If trapezoid KLMN shown below is reflected across the x-axis to form trapezoid K L M N, what are the apparent coordinates of M? A. (1, 3) B. (3, 1) C. (4, 6). (6, 4) A. ( 4, 5) B. ( 4, 5) C. (4, 5). (4, 5) page 8
9 12. XYZ is translated 3 units to the right and 2 units down. 13. What is the image of R when RSTU is translated 3 units down and 6 units right? What will be the apparent coordinates of the image of point X? A. ( 1, 1) B. (1, 1) C. (1, 4). (4, 1) A. (0, 8) B. (3, 5) C. (5, 3). (8, 0) page 9
10 14. Study RST on the grid below. 16. Trapezoid ABC below is to be translated to trapezoid A B C by the following motion rule. (x, y) (x + 3, y 4) When RST is translated 4 units down, what are the apparent coordinate of T? A. ( 8, 1) B. ( 4, 1) C. ( 1, 8). (0, 4) What will be the coordinates of vertex C? A. (1, 3) B. (2, 1) C. (6, 1). (8, 3) 15. The vertices of ABC are A(2, 1), B(3, 4), and C(1, 3). If ABC is translated 1 unit down and 3 units to the left to create EF, what are the coordinates of the vertices of EF? A. (0, 1), E(1, 2), F(1, 3) B. (0, 1), E(0, 3), F( 2, 2) C. ( 2, 2), E(0, 3), F( 1, 0). ( 1, 0), E(0, 3), F( 2, 2) 17. Which expression describes the translation of a point from ( 3, 4) to (4, 1) A. 7 units left and 5 units up B. 7 units right and 5 units up C. 7 units left and 5 units down. 7 units right and 5 units down page 10
11 Use the diagram below to answer the question that follows. Triangle RST is shown. Triangle RST is translated 8 units to the left and 2 units down to create triangle R S T. a) raw and label triangle R S T. Then, triangle R S T is reflected across the x-axis to create triangle R S T What will be the coordinates of point A if figure ABC is reflected across the x-axis? b) raw and label triangle R S T 19. Triangle PQR was reflected over the x-axis and then translated 7 units to the right to create P Q R as shown. 21. Use the figure below to answer the question that follows. raw original triangle PQR and label the vertices. A graphic artist needs to reflect triangle ABC across the x-axis to create Figure A B C. What are the coordinates of A? A. (1, 2) B. (2, 1) C. ( 1, 2). ( 2, 1) page 11
12 22. Triangle ABC has the vertices A(2, 0), B(4, 2), and C(3, 4). Name the ordered pair of C after a reflection across the x-axis. 23. Use the graphic below to answer the question. Rectangle WXYZ will be transformed so that W is located at ( 3, 1) and Z is located at (2, 1). Which could be the coordinates of X and Y so that W X Y Z is congruent to WXYZ? A. X is located at ( 3, 6) and Y is located at (2, 6) B. X is located at (3, 8) and Y is located at ( 2, 8) C. X is located at ( 3, 6) and Y is located at (2, 6). X is located at (2, 8) and Y is located at ( 3, 8) page 12
13 24. Zane graphed a parallelogram on the coordinate grid shown. Zane then translated the parallelogram up 5 units. Which coordinate grid shows the figure after the translation? A. B. C.. page 13
14 25. Sherry drew PQR and line m, as shown on the grid below. 27. Isaac is going to draw STU on the grid shown below so that it is congruent to PQR. Sherry will reflect PQR over line m. What will be the coordinates of the image of point R after PQR is reflected over line m? A. (5, 6) B. (6, 9) C. (7, 6). (9, 6) He located point S at ( 1, 0) and point T at ( 4, 4). Which of the following coordinates represents a possible location for point U? A. ( 3, 6) B. ( 3, 7) C. ( 4, 3). ( 4, 7) 26. If Figure ABC is translated so that the image of A is A at ( 3, 2), then the coordinates of the image of point B will be A. (0, 0). B. ( 1, 4). C. ( 2, 1).. ( 3, 1). page 14
15 28. The diagram below shows PQR on a coordinate plane. 29. Triangle ABC has vertices at A(3, 3), B(1, 1), and C(2, 5). In which of the graphs below is triangle A B C a reflection of triangle ABC over the y-axis? A. Which of the following is the result of a reflection of PQR? A. B. B. C. C... page 15
16 30. Quadrilateral EFGH is shown on the coordinate grid below. 31. Triangle R S T is shown on the coordinate grid below. The quadrilateral will be reflected over the y-axis. The reflected image will then be translated 2 units left and 7 units up. In which of the following quadrants will the final reflected and translated image lie? A. I and II B. II and III C. II and IV. III and IV Triangle R S T is the image of triangle RST after triangle RST was translated 3 units to the right and 4 units up. What were the coordinates of point R before the translation? A. (6, 6) B. (5, 7) C. ( 2, 0). ( 1, 1) page 16
17 32. Joanne and Christopher are designing a quilt. They start by creating a triangle shape in the lower left quadrant as shown below. They transform it by rotating the triangle shown above 90 clockwise about the origin. What does the new design look like? A. B. C.. page 17
18 33. Polygon A will be rotated counter-clockwise 90 about point P to form polygon A. A. B. C.. page 18
19 34. Triangle PQR is shown. 35. If triangle ABC is rotated 180 degrees about the origin, what are the coordinates of A? What are the coordinates of P when PQR is dilated by a scale factor of 3 using the origin as the center? A. ( 5, 4) B. ( 5, 4) A. (6, 18) B. ( 3, 2 ) 3 C. ( 4, 5). ( 4, 5) C. ( ) 2 3, 3. (18, 6) 36. Pentagon JKLMN is shown on the coordinate grid. The pentagon is rotated 90 counterclockwise about the origin to create pentagon J K L M N. raw and label pentagon J K L M N. page 19
20 37. Figure LMNO is shown below. 38. Which diagram below best shows a rotation of the pre-image to the image? A. Figure L M N O will be created by rotating figure LMNO 90 clockwise about point M. B. What will be the coordinates of point L? A. (0, 6) B. (2, 6) C. (3, 3). (3, 5) C.. page 20
21 39. Larry used pieces of pipe to build this shape. 41. Which of the diagrams below best shows a translation of ( 4) units of the dark triangle? A. Which picture shows Larry s shape turned 90 counterclockwise? A. B. B. C.. C Which of the following shows the flag above turned 90 clockwise? A. B. C.. page 21
22 42. The figure below depicts a coordinate plane, rectangle PQRS, and the image of rectangle PQRS after a transformation. Point P is the image of point P, Q is the image of Q, R is the image of R, and S is the image of S. 43. Select all transformations from the list below that could transform the original to the image in the coordinate grid below? Which transformation produced the image P Q R S? A. a 180-degree counterclockwise rotation about the point (0, 0) B. a translation of four units to the right C. a 90-degree counterclockwise rotation about the point (0, 0). a reflection over the y-axis A. Rotate 180 about the origin. B. Rotate 90 clockwise about the origin, translate down 6 units C. Rotate 90 counterclockwise about the origin, translate down 6 units. Rotate 90 counterclockwise about the origin, translate down 1 unit and right 6 units E. Rotate 90 counterclockwise about the origin, translate down 6 units and left 1 unit F. Rotate 90 counterclockwise about the origin, translate down 1 unit, reflect over the y-axis G. Rotate 90 clockwise about the origin, translate down 1 unit, reflect over the y-axis page 22
23 44. Janet graphed a triangle on the coordinate grid shown. 45. Use the graph to answer the question. Janet rotated the triangle 90 clockwise about the origin to create figure A B C. What are the coordinates of the vertices of the figure A B C after the rotation? Which pair of transformations moves quadrilateral 1 to quadrilateral 2? A. A ( 4, 4) B ( 4, 2) C ( 1, 2) C. A ( 4, 4) B ( 2, 4) C ( 2, 1) B. A (4, 4) B (2, 4) C (2, 1). A (4, 4) B (4, 2) C (1, 2) A. reflect it over the line y = 3, then rotate it 90 counterclockwise about the origin B. reflect it over the x-axis, then rotate it 180 about the origin C. rotate it 90 counterclockwise about point ( 3, 3), then translate it 8 units to the right. translate it 8 units to the right, then reflect it over the line y = 3 page 23
24 46. ABC and EF are shown on the grid below. 47. In the graph below, figure M was rotated clockwise about the origin to generate figure T. Which of the following transformations will map ABC onto EF? A. Reflect ABC over the y-axis and shift up 6 spaces. What was the angle of rotation of figure M about the origin? A. 90 B. 180 C B. Reflect ABC over the x-axis and shift up 6 spaces. C. Reflect ABC over the y-axis and shift down 6 spaces.. Reflect ABC over the y-axis, reflect over the x-axis, and shift down 4 spaces. page 24
25 48. Look at LMN on the coordinate plane. Which coordinate plane shows LMN after a 90 counterclockwise rotation about the origin? A. B. C.. page 25
26 49. A dilation with center P maps the rectangle RSTU to the rectangle R S T U as shown below. What is the scale factor of this dilation? A. 2 B. 3 C page 26
27 50. Which of the following shows a triangle and the 180 rotation of the triangle about the origin? A. B. C.. page 27
28 51. Ann rotates this triangle 90 clockwise. 52. Quadrilateral STVR is graphed on the coordinate plane below. Which choice shows Ann s triangle after the 90 rotation? A. B. C. Quadrilateral STVR will be rotated 90 clockwise about the origin (0, 0). What will be the new coordinates of point R? A. ( 5, 3) B. ( 3, 5) C. (3, 5). (5, 3). page 28
29 Problem-Attic format version c EducAide Software Licensed for use by Brenda Perachi Terms of Use at 02/10/ C A A A A C C C C Triangle R S T correctly with vertices at R ( 7, 2), S ( 5, 5), and T ( 2, 1) and triangle R S T correctly labeled (-2,-5) 21. For this item, the response correctly: Shows triangle PQR with the vertices at the correct coordinates: P( 1, 1), Q( 4, 3) and R( 2, 5). AN labels the vertices of triangle PQR. Ex: A 22. C (3, 4) C B A B B C B B
30 Teacher s Key Page A a labeled pentagon with vertices at N( 2, 2), J( 5, 2), K( 6, 4), L( 4, 4), M( 2, 6) A A B C C B,, F A A B C
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