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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.
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 2
12.
13. 6 units up.
14.
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 3
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16. 3 units to the left and 2 units up.
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 4
10.2 Graphs of Translations
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 5
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 6
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 7
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 8
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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)
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.
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 11
10.5 Graphs of Reflections
Answers
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 12
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 13
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 14
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 15
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 16
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 17
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 18
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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
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°.
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 21
10.8 Graphs of Rotations
Answers
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 22
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 23
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 24
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 25
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 26
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 27
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 28
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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°
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).
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 31
10.11 Graphs of Dilations
Answers
1.
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3.
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 32
4.
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 33
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 34
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 35
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 36
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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
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.
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 39
10.14 Order of Composite Transformations
Answers
1.
2.
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.
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 41
7.
8. Rotation 90 degree clockwise about the origin.
9.
Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 42
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Chapter 10 – Geometric Transformations Answer Key
CK-12 Algebra I Honors Concepts 43
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15. The transformations were different because the order of transformations matters.
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°
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)
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′′