Geometry Mathematician: ________________________________ Unit 2 Transformations Period:___________ Unit 2 Review Target 1: Identify and determine congruent parts given a rigid motion. Directions: Select all that apply given the following information. 1) βπππ β βπππ (a) ππ β ππ (b) β π β β π (c) βπππ β βπππ (d) ππ β ππ (e) ππ β ππ
2) βπ΄π΅πΆ β βπ½πΎπΏ (a) π΅πΆ β πΏπΎ (b) β π΅ β β πΏ (c) βπ΅πΆπ΄ β βπΎπ½πΏ (d) πΆπ΄ β π½πΎ (e) β πΆ β β πΏ
Directions: List three real life examples that would relate to the given rigid motion. 3) Transformation ____________________________________
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4) Rotation ____________________________________
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5) Reflection ____________________________________
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Directions: Determine if the following are examples of rigid motion. If not, explain why. 6) and Rigid Motion? YES or NO If no, explain why: __________________ ________________________________________ ________________________________________
7) and Rigid Motion? YES or NO If no, explain why: __________________ ________________________________________ ________________________________________
8)
Q and Q Rigid Motion? YES or NO If no, explain why: __________________ ________________________________________ ________________________________________
9) βπΏππ has coordinates πΏ β2,4 , π β4,1 , and π(β3,5) and βπππ has coordinates π 0,0 ,π β2,β3 , and π β1,1 . Which of the following statements are true? Select all that apply! (a) The triangles are rigid motions of each other (b) The triangles represent a reflection (c) The triangles represent a translation (d) β πΏ β β π (e) ππ β ππ
10) βπ΄π΅πΆ has coordinates π΄ β6,β1 , π΅ β2,β1 , and πΆ(β4,β4) and βπππ has coordinates π 1,β6 ,π 1,β2 , and π 4,β4 . Which of the following statements are true? Select all that apply! (a) The triangles are rigid motions of each other (b) The triangles represent a rotation (c) The triangles represent a reflection (d) β π΅ β β π (e) π΄πΆ β ππ
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Target 2: Perform and identify rigid transformations of points, segments, and figures. 11) Directions: You and a friend are walking around Chicago. Each location is shown on the map. Determine what the translation would be given you are traveling from the first location to the second location (in blocks).
a) #1 β #2 Rule: π₯, π¦ β (π₯________, π¦_________)
b) #2 β #3 Rule: π₯, π¦ β (π₯________, π¦_________)
c) #3 β #4 Rule: π₯, π¦ β (π₯________, π¦_________)
d) #3 β #1 Rule: π₯, π¦ β (π₯________, π¦_________)
12) When a figure is translated π₯, π¦ β (π₯ + 10, π¦) which of the following applies? Select ALL that apply. (a) Translation is a rigid motion (b) Translation is a non-Ββrigid motion (c) Figure is moved down (d) Figure is moved right (e) Figure is moved left
13) When a figure is translated π₯, π¦ β (π₯ β 1, π¦ β 7) which of the following applies? Select ALL that apply. (a) Translation is a rigid motion (b) Translation is a non-Ββrigid motion (c) Figure is moved down (d) Figure is moved right (e) Figure is moved left
14) A point πΎ(5,β7) is being rotated clockwise about the origin 90Β°. What are the coordinates of the image of πΎ?
15) A point π(8,1) is being rotated counterclockwise about the origin 180Β°. What are the coordinates of the image of π?
16) Rotate ππΏ 90Β° counterclockwise about the origin. The coordinates are π(β4,2) and πΏ(β2,7). Which of the following statements are true? (a) πβ² will be located in quadrant III (b) πΏβ² will be located in quadrant I (c) πΏβ² will be located in quadrant III (d) The slope of πβ²πΏβ² is negative (e) The slope of πβ²πΏβ² is positive
17) Rotate π΄π΅ 270Β° clockwise about the origin. The coordinates are π΄(β3,6) and π΅(β2,1). Which of the following statements are true? (a) π΄β² will be located in quadrant III (b) π΄β² will be located in quadrant II (c) π΅β² will be located in quadrant III (d) The slope of π΄β²π΅β² is negative (e) The slope of π΄β²π΅β² is positive
18) A line segment has endpoints A (5, -Ββ1) and B (-Ββ6, -Ββ2). The line segment is reflected over x = 1. Which statements are true? Select all that apply.
(a) Sum of π΄! = β2 (b) Sum of π΄! = 4 (c) Sum of π΄! = β4 (d) Sum of π΅! = 6 (e) Sum of π΅! = 10
A (5, -Ββ1) B(-Ββ6, -Ββ2) Aβ ( , ) Bβ ( , ) Sum of Aβ = Sum of Bβ =
19) A line segment has endpoints A (5,0) and B (2, 6). The line segment is reflected over y = 3. Which statements are true? Select all that apply.
(a) Sum of π΄! = β1 (b) Sum of π΄! = 11 (c) Sum of π΄! = 17 (d) Sum of π΅! = 0 (e) Sum of π΅! = 2
A (5, 0) B(2, 6) Aβ ( , ) Bβ ( , ) Sum of Aβ = Sum of Bβ =
Target 3: Perform multiple transformations to determine coordinates and location of image. Directions: Complete the compositions of functions for the given problems. 20) π»(β3,4)
β’ Rotate 180Β° ccw about the origin
β’ Then, reflect over π¦ = β2
What is the location of point π»"?
21) πΊ(6,7)
β’ Translate up 3 units and left 5 units
β’ Then, reflect over π₯ = 4
What is the location of point πΊ"?
22) Line segment π΄π΅ has the coordinates of π΄(4,0) and π΅(6,β5). The line segment is translated up 6 units and right 1 unit. Then the line segment is reflected over the x-Ββaxis. Find the coordinates of π΅". Then add the coordinates. Bββ x-Ββcoordinate: _________ Bββ y-Ββcoordinate: ___________ Sum: _____________
23) Line segment ππ has the coordinates of π(β2,1) and π(β4,β3). The line segment is translated down 2 units and left 3 unit. Then the line segment is reflected over the y-Ββaxis. Find the coordinates of π". Then add the coordinates. Mββ x-Ββcoordinate: __________ Mββ y-Ββcoordinate: __________ Sum: _____________
Directions: Describe the composition of functions in the graph for each problem. 24)
First transformation: _________________________________________ Second transformation: ________________________________________
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First transformation: _________________________________________ Second transformation: ________________________________________
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First transformation: _________________________________________ Second transformation: ________________________________________
27) Directions: Which of the following transformations will result in the same outcome when transforming π β3,4 ? First transformation: Reflection over the x-Ββaxis Second transformation: Rotation 90Β° clockwise about the origin SELECT ALL THAT APPLY:
First Transformation Second Transformation (a) Reflection over the x-Ββaxis Rotation 270Β° cw about the origin (b) Reflection over the x-Ββaxis Rotation 270Β°ccw about the origin (c) Reflection over the y-Ββaxis Rotation 90Β° ccw about the origin (d) Rotation 270Β° ccw about the origin Reflection over the x-Ββaxis (e) Rotation 90Β° ccw about the origin Reflection over the y-Ββaxis (f) Rotation 270Β° cw about the origin Reflection over the y-Ββaxis 28) Find three examples of real life situations that will use at least two transformations. Then describe why. a) Example 1:
b) Example 2:
c) Example 3:
Unit 2 Review Answers
1. A,B,D 2. E 3. Answers may vary (examples: Hockey puck sliding down the ice, plane flying through the
air, stc.) 4. Answers may vary (examples: ferris wheel, bike wheel, etc.) 5. Answers may vary (examples: images in a lake, images in a mirror, etc.) 6. YES (reflection) 7. YES ( 180Λ rotation) 8. NO β this is a dilation (the size changes so not a rigid motion) 9. A, C, E 10. A, B, D 11.
a. π₯,π¦ β (π₯ β 1,π¦ + 2) b. π₯,π¦ β (π₯ + 3,π¦) c. π₯,π¦ β (π₯ + 1,π¦ β 2) d. π₯,π¦ β (π₯ β 2,π¦ β 3)
12. A, D 13. A, C, E 14. Kβ(-Ββ7,-Ββ5) 15. Mβ(8,-Ββ1) 16. A, C, D 17. A, C, E 18. C, D 19. B, E 20. Hββ(3,0) 21. Gββ(7,10) 22. Bββ x-Ββcoordinate: 7, Bββ y-Ββcoordinate: -Ββ1, SUM = 6 23. Mββ x-Ββcoordinate: -Ββ5 , Mββ y-Ββcoordinate: -Ββ1 , SUM =-Ββ6 24. #1 β Rotation 90Λ CW about the origin
#2 β Reflection over the x-Ββaxis 25. #1 β 180Λ rotation CW/CCW about the origin
#2 β y-Ββaxis reflection 26. #1 -Ββ Translation π₯,π¦ β (π₯,π¦ + 10)
#2 β Reflection over the y-Ββaxis 27. B, C, E 28.
a. Answers may vary b. Answers may vary c. Answers may vary