10.1 Translations
Transcript of 10.1 Translations
![Page 1: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/1.jpg)
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.
2. 5 units to the right and 6 units down.
3. 7 units to the right and 4 units up.
4. 9 units to the right and 2 units up.
5. 6 units left and 3 units down.
6. 5 units to the right and 3 units up.
7. 3 units to the right and 5 units down.
8. 8 units to the right.
9. 3 units to the left and 4 units up.
10. 11 units to the right and 7 units up.
11.
![Page 2: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/2.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 2
12.
13. 6 units up.
14.
![Page 3: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/3.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 3
15.
16. 3 units to the left and 2 units up.
![Page 4: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/4.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 4
10.2 Graphs of Translations
Answers
1.
2.
3.
4.
![Page 5: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/5.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 5
5.
6.
7.
![Page 6: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/6.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 6
8.
9.
10.
![Page 7: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/7.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 7
11.
12.
13.
![Page 8: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/8.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 8
14.
15.
16.
![Page 9: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/9.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 9
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)
![Page 10: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/10.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 10
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.
![Page 11: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/11.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 11
10.5 Graphs of Reflections
Answers
1.
2.
3.
![Page 12: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/12.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 12
4.
5.
6.
![Page 13: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/13.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 13
7.
8.
9.
![Page 14: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/14.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 14
10.
11.
12.
![Page 15: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/15.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 15
13.
14.
15.
![Page 16: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/16.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 16
16.
17.
18.
![Page 17: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/17.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 17
19.
20.
21.
![Page 18: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/18.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 18
22.
23.
24.
![Page 19: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/19.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 19
10.6 Rules for Reflections
Answers
1. 𝑟𝑦−𝑎𝑥𝑖𝑠
2. 𝑟𝑦−𝑎𝑥𝑖𝑠
3. 𝑟𝑥−𝑎𝑥𝑖𝑠
4. 𝑟𝑦=−𝑥
5. 𝑟𝑦=𝑥
6. 𝑟𝑦−𝑎𝑥𝑖𝑠
7. 𝑟𝑦=𝑥
8. 𝑟𝑦=−𝑥
9. 𝑟𝑦−𝑎𝑥𝑖𝑠
10. 𝑟𝑥−𝑎𝑥𝑖𝑠
11. 𝑟𝑥−𝑎𝑥𝑖𝑠
12. 𝑟𝑦−𝑎𝑥𝑖𝑠
13. 𝑟𝑦=𝑥
14. 𝑟𝑦=−𝑥
15. 𝑟𝑦−𝑎𝑥𝑖𝑠
![Page 20: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/20.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 20
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°.
![Page 21: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/21.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 21
10.8 Graphs of Rotations
Answers
1.
2.
3.
![Page 22: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/22.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 22
4.
5.
6.
![Page 23: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/23.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 23
7.
8.
9.
![Page 24: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/24.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 24
10.
11.
12.
![Page 25: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/25.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 25
13.
14.
15.
![Page 26: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/26.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 26
16.
17.
18.
![Page 27: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/27.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 27
19.
20.
21.
![Page 28: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/28.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 28
22.
23.
24.
![Page 29: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/29.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 29
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°
![Page 30: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/30.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 30
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).
![Page 31: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/31.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 31
10.11 Graphs of Dilations
Answers
1.
2.
3.
![Page 32: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/32.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 32
4.
5.
6.
![Page 33: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/33.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 33
7.
8.
9.
![Page 34: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/34.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 34
10.
11.
12.
![Page 35: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/35.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 35
13.
14.
15.
![Page 36: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/36.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 36
16.
![Page 37: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/37.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 37
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
![Page 38: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/38.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 38
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.
![Page 39: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/39.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 39
10.14 Order of Composite Transformations
Answers
1.
2.
![Page 40: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/40.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 40
3.
4. 180 degree rotation
5.
6. Translation 12 to the right.
![Page 41: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/41.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 41
7.
8. Rotation 90 degree clockwise about the origin.
9.
![Page 42: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/42.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 42
10.
11.
12.
![Page 43: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/43.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 43
13.
14.
15. The transformations were different because the order of transformations matters.
![Page 44: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/44.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 44
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°
![Page 45: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/45.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 45
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)
![Page 46: 10.1 Translations](https://reader030.fdocuments.in/reader030/viewer/2022012410/616a594c11a7b741a351860d/html5/thumbnails/46.jpg)
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 46
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′′