10.1 translations

Chapter 10 – Geometric Transformations Answer Key

CK-12 Algebra I Honors Concepts 1

10.1 Translations

Answers

1. 3 units to the right and 5 units down.


3. 7 units to the right and 4 units up.


5. 6 units left and 3 units down.



8. 8 units to the right.

9. 3 units to the left and 4 units up.


11.



12.

13. 6 units up.

14.



15.

16. 3 units to the left and 2 units up.



10.2 Graphs of Translations

Answers

1.

2.

3.

4.



5.

6.

7.



8.

9.

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11.

12.

13.



14.

15.

16.



10.3 Rules for Translations

Answers

1. (𝑥, 𝑦) → (𝑥 + 1, 𝑦 + 2)

2. (𝑥, 𝑦) → (𝑥 + 2, 𝑦 + 2)

3. (𝑥, 𝑦) → (𝑥 − 8, 𝑦 + 8)

4. (𝑥, 𝑦) → (𝑥 − 6, 𝑦 + 6)

5. (𝑥, 𝑦) → (𝑥 + 6, 𝑦)

6. (𝑥, 𝑦) → (𝑥, 𝑦 + 2)

7. (𝑥, 𝑦) → (𝑥 + 2, 𝑦 + 7)

8. (𝑥, 𝑦) → (𝑥 − 8, 𝑦 + 3)

9. (𝑥, 𝑦) → (𝑥 − 10, 𝑦 + 4)

10. (𝑥, 𝑦) → (𝑥 + 7, 𝑦 + 1)

11. (𝑥, 𝑦) → (𝑥 + 5, 𝑦 − 4)

12. (𝑥, 𝑦) → (𝑥 − 4, 𝑦 − 6)

13. (𝑥, 𝑦) → (𝑥 + 7, 𝑦 + 3)

14. (𝑥, 𝑦) → (𝑥 + 5, 𝑦 − 6)

15. (𝑥, 𝑦) → (𝑥 − 4, 𝑦 + 7)



10.4 Reflections

Answers

1. (3, −1)

2. (4, 2)

3. (−5, −3)

4. (−6, −4)

5. (4, 3)

6. (−5, − 4)

7. (5, −4)

8. (−3, 3)

9. (1, 3)

10. (−2, 4)

11. (3, −5)

12. (4, −6)

13. Reflection across the x-axis.

14. Reflection across the y-axis.

15. Reflection across the line y=x.



10.5 Graphs of Reflections

Answers

1.

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4.

5.

6.



7.

8.

9.



10.

11.

12.



13.

14.

15.



16.

17.

18.



19.

20.

21.



22.

23.

24.



10.6 Rules for Reflections

Answers

1. 𝑟𝑦−𝑎𝑥𝑖𝑠


3. 𝑟𝑥−𝑎𝑥𝑖𝑠

4. 𝑟𝑦=−𝑥

5. 𝑟𝑦=𝑥


7. 𝑟𝑦=𝑥

8. 𝑟𝑦=−𝑥





13. 𝑟𝑦=𝑥

14. 𝑟𝑦=−𝑥




10.7 Rotations

Answers

1. (−3, −1)

2. (−4, 2)

3. (5, −3)

4. (6, −4)

5. (3, 3)

6. (3, 4)

7. (4, −5)

8. (−4, 5)

9. (3, −3)

10. (−9, 8)

11. 90°𝐶𝐶𝑊 about the origin.

12. 270°𝐶𝐶𝑊 about the origin.

13. 200°𝐶𝑊 about point B.

14. 100°𝐶𝑊 about point F.

15. 180°𝐶𝑊 is the same as 180°𝐶𝐶𝑊 because a full circle (one complete rotation) is 180° + 180° =

360°.



10.8 Graphs of Rotations

Answers

1.

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16.

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19.

20.

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22.

23.

24.



10.9 Rules for Rotations

Answers

90° rotation 180° rotation 270° rotation 360° rotation

1. (1,4) (-4, 1) (-1, -4) (4, -1) (1,4)

2. (4, 2) (-2, 4) (-4, -2) (2, -4) (4, 2)

3. (2, 0) (0, 2) (-2, 0) (0, -2) (2, 0)

4. (-1, 2) (-2, -1) (1, -2) (2, 1) (-1, 2)

5. (-2, -3) (3, 2) (2, 3) (3, 2) (-2, -3)

6.𝑅180°

7. 𝑅270°

8. 𝑅90°

9. 𝑅270°

10. 𝑅180°

11. 𝑅90°

12. 𝑅270°

13. 𝑅45°

14. 𝑅135°

15. 𝑅220°



10.10 Dilations

Answers

1. 24 cm

2. 5 cm

3. 12 cm

4. 54 cm

5. 10 cm

6. 12 cm

7. 8 cm

8. 6 cm

9. 80 cm

10. 50 cm

11. Triangle ABC is dilated by a factor of 2 from the center point of the origin.

12. The preimage is dilated by a factor of 1

3 from the center point of the origin.

13. The preimage is dilated by a factor of 1

5 from the center point of the origin.

14. Triangle LMO is dilated by a factor of 2 from center point D.

15. Quadrilateral BCDE is dilated by a factor of 3 from center point (1, 2).



10.11 Graphs of Dilations

Answers

1.

2.

3.



4.

5.

6.



7.

8.

9.



10.

11.

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13.

14.

15.



16.



10.12 Rules for Dilations

Answers

𝐷2 𝐷5 𝐷12

𝐷34

1. (1,4) (2, 8) (5, 20) (

1

2, 2) (

3

4, 3)

2. (4, 2) (8, 4) (20, 10) (2, 1) (3,

3

2)

3. (2, 0) (4, 0) (10, 0) (1, 0) (

3

2, 0)

4. (-1, 2) (-2,4 ) (-5, 10) (−

1

2, 1) (−

3

4,3

2)

5. (-2, -3) (-4, -6) (-10, -15) (−1, −

3

2) (

3

2, −

9

4)

6. (9, 4) (18, 8) (45, 20) (

9

2, 2) (

27

4, 3)

7. (-1, 3) (-2, 6) (-5, -15) (−

1

2,3

2) (−

3

4,9

4)

8. (-5, 2) (-10, 4) (-25, 10) (−

5

2, 1) (−

15

4,3

2)

9. (2, 6) (4, 12) (10, 30) (1, 3) (

3

2,9

2)

10. (-5, 7) (-10, 14) (-30, 35) (−

5

2,7

2) (−

15

4,21

4)

11. 𝐷2

12. 𝐷3

13. 𝐷3

4

14. 𝐷1

2

15. 𝐷3

2



10.13 Composite Transformations

Answers

1. X'(1, -8) and X''(5, -2)

2. A'(-1, 2) and A''(-1, -2)

3. P'(6, -5) and P''(-5, -6)

4. J'(2,5), T'(-2,-3) and J''(8,2), T''(4,-6)

5. S'(2,-5),K'(4,5) and S''(5,2), K''(-5,-4)

6. K'(4,-1) and K''(1,4)

7. Rotation 180 degrees about point B followed by a translation to the left 4 and down 6.

8. Translation right 7 and 4 up followed by a reflection across the x-axis.

9. Rotation 90 degrees clockwise about point D followed by a translation to the right 2 and up 4.

10. Reflection across the x-axis followed by a reflection across the line 𝑦 = 𝑥.

11. Translation to the right 10 and up 1 followed by a reflection across the x-axis.

12. Translation

13. Rotation

14. 180 degree rotation

15. Because it's like a reflection that has slid.



10.14 Order of Composite Transformations

Answers

1.

2.



3.

4. 180 degree rotation

5.

6. Translation 12 to the right.



7.

8. Rotation 90 degree clockwise about the origin.

9.



10.

11.

12.



13.

14.

15. The transformations were different because the order of transformations matters.



10.15 Notation for Composite Transformations

Answers

𝑇3,−4 ∘ 𝑅90° 𝑟𝑥−𝑎𝑥𝑖𝑠 ∘ 𝑟𝑦−𝑎𝑥𝑖𝑠 𝑇1,6 ∘ 𝑟𝑥−𝑎𝑥𝑖𝑠 𝑟𝑦−𝑎𝑥𝑖𝑠 ∘ 𝑅180°

1. (1,4) (-1, -3) (-1,-4) (2,2) (1,-4)

2. (4,2) (1,0) (-4,-2) (5,4) (4,-2)

3. (2,0) (3, -2) (-2,0) (3,6) (2,0)

4. (-1,2) (1, -5) (1,-2) (0,4) (-1,-2)

5. (-2,-3) (0, -6) (2,3) (-1,9) (-2,3)

6. (4,-1) (2,0) (-4,1) (5,7) (4,1)

7. (3,-2) (5, -1) (-3,2) (4,8) (3,2)

8. (5,4) (-3,1) (-5,-4) (6,2) (5,-4)

9. (-3, 7) (-4, -7) (3, -7) (-2,-1) (-3, -7)

10. (0,0) (3,-4) (0,0) (1,6) (0,0)

11. 𝑅180° ∘ 𝑇−4,−6

12. 𝑇5,6 ∘ 𝑟𝑦−𝑎𝑥𝑖𝑠

13. 𝑇8,−2 ∘ 𝑟𝑦−𝑎𝑥𝑖𝑠

14. 𝑅90° ∘ 𝑅180°

15. 𝑟𝑥=2 ∘ 𝑇10,2.4 ∘ 𝑅90°



10.16 The Midpoint Formula

Answers

1. (4, 8)

2. (4, 5)

3. (3.5, 5.5)

4. (5.5, 6.5)

5. (4.5, 4)

6. (1, 6)

7. (11, 19)

8. (6, 14)

9. (4, −4)

10. (14, −5)

11. (2, 17)

12. (0, 2); (3, 0.5); (0, −1.5)

13. (−8, 1); (−4, −3)

14. (−5.6, 2.65)

15. (−4,1); (1.5, −2); (1.5,4); (7,1)



10.17 The Distance Formula

Answers

1. 2√2

2. 2√10

3. √2

4. √130

5. √85

6. √5

7. √89

8. 2√17

9. 2.6

10. √85

11. √29

12. 𝑆𝑇 = √17; 𝑆′𝑇′ = √17; 𝑆′′𝑇′′ = √17

13. 𝐺𝐸 = √34; 𝐺′𝐸′ = √34; 𝐺𝐹 = 2√13; 𝐺′𝐹′ = 2√13 ; 𝐸𝐹 = 5√2; 𝐸′𝐹′ = 5√2

14. 𝐶𝐷 = 𝐶′𝐷′ = 𝐷𝐸 = 𝐷′𝐸′ = 𝐻𝐺 = 𝐻′𝐺′ = 𝐺𝐹 = 𝐺′𝐹′ = 2; 𝐺𝐷 = 𝐺′𝐷′ = 3

15. 𝐴𝐵 = 2√2 = 𝐴′𝐵′ = 𝐴′′𝐵′′; 𝐵𝐶 = √2 = 𝐵′𝐶′ = 𝐵′′𝐶′′; 𝐶𝐷 = 1 = 𝐶′𝐷′ = 𝐶′′𝐷′′; 𝐷𝐴 = 3 =

𝐷′𝐴′ = 𝐷′′𝐴′′

10.1 translations

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