20 y x 2 6 5 4 3 2 1 y y x 65 4 3 2 1 1 2 3 4 5 6 1 2 3 4 5 6 x y 2 6-4 Point Reflection and Symmetry (pages 103–104) 1 (2) H 2 (1) only line symmetry 3 (3) both point and line symmetry 4 (3) (k, 2k) 5 line symmetry 6 both 7 point symmetry 8 both 9 (1, 3) 10 (3, 1) 11 (9, 0) 12 (2, 6) 13 (4, 4) 14 (8, 2) 15 (2, 4) 16 (2, 8) 17 (10, 10) 18 Point reflection is a trans<strong>for</strong>mation of a figure into ano<strong>the</strong>r figure. Point symmetry is a quality of a figure. A figure with point symmetry is not changed by a reflection through that point. (It is rotated in ei<strong>the</strong>r direction 180 about a point.) x 6-5 Rotations (page 107) 1 (2) trapezoid 2 (1) regular hexagon 3 (2) regular pentagon 4 (2) rectangle 5 (1) equilateral triangle 6 (1) 7 Z 8 X 9 Y 10 Z 11 (1, 5) 12 (3, 3) 13 (2, 8) 14 (2, 3) 15 (2, 2) 16 (4, 4) 17 (6, 3) 18 (2, 6) 19 (5, 5) 20 W(3, 2), H(8, 2), Y(5, 10) 6-6 Dilations (page 110) 1 (3) (4, 10) 2 (2) 1 _ 2 3 (4) (x, y) → (2x, 2y) 4 (4) 20 square inches 5 (6, 9) 9 6 ( 3, _ 2 ) or (3, 4.5) 7 (4, 6) For problems 8–11, see figure below. 8 A(0, 8), B(2, 2), C(6, 4) 9 A(0, 3), B ( 3 _ , 4 3 _ 4 ) , C ( 2 1 _ , 1 4 1 _ 2 ) 10 A(0, 12), B(3, 3), C(9, 6) 6-6 Dilations 31
11 A(0, 8), B(2, 2), C(6, 4) (8) 10 9 8 7 6 5 A 4 3 C B 2 1 109 8 7 6 5 4 3 2 1 1 2 3 1 2 (9) 3 4 5 6 7 8 9 10 4 5 6 (11) 7 8 9 10 11 12 13 14 (10) y 12 (1, √ 3 ) 13 ( √ 2 _ , 2 √ 2 _ 2 ) 14 (3a, 3b) 15 k 1 _ ; (2, 4) → (1, 2) 3 16 k 1 _ ; (2, 4) → (1, 2) 2 17 (3, 12) 18 G(1, 1), N(4, 1), A(4, 1), T(1, 1) 6-7 Properties Under Trans<strong>for</strong>mations (pages 111–113) 1 (2) dilation 2 (4) dilation 3 (2) translation 4 (2) r y x 5 (3) dilation D 1 6 r y-axis 7 T 5, 0 8 R 270 or R 90 9 T 4, 3 32 Chapter 6: Trans<strong>for</strong>mations and <strong>the</strong> Coordinate Plane x 10 11 12 13 8 7 6 5 4 3 2 y 1 x 8 7 6 5 4 3 2 1 1 K'(2, 2) 1 2 3 4 K(2, 2) 5 6 7 8 M'(5, 2) 2 3 M(5, 2) 4 Z'(3, 4) 5 6 7 8 Z(3, 4) direct isometry y 8 7 6 5 4 3 K'(1, 1) 2 1 M'(2, 1) x 8 7 6 5 4 3 2 1 1 2 3 4 1 Z'(0, 1) 5 6 7 8 2 K(2, 2) 3 M(5, 2) 4 5 6 7 8 Z(3, 4) direct isometry 5 4 3 2 y 1 x 5 4 3 2 1 1 1 2 3 4 5 6 7 8 9 10 11 12 K(2, 2 2) M(5, 2) 3 4 5 K'(4, 4) Z(3, 4) W'(10, 4) 6 7 8 9 10 not an isometry A''' R" A" R''' C''' C" Z'(6, 8) y 10 9 8 7 6 5 4 3 2 1 109 8 7 6 5 4 3 2 1 1 C 2 1 2 3 4 R 5 6 7 8 9 10 3 4 A 5 6 C' R' 7 8 9 10 A' a C(3, 5), A(4, 7), R(7, 4) x
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27 1. Common external tangents, −
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8. mHCT 1 _ m 2 TH mCHT 1 _ CT 2
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16 a (2 √ 2 , 2 √ 2 ), (2 √
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15 a Use constructing a congruent a
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5 Two horizontal lines y 11 and y
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Each review has a total of 58 possi
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Part III For each question, use the
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Chapters 1-3 (pages 438-441) Part I
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Part IV For each question, use the
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16 Score Explanation 4 a 91, b 35
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Chapters 1-5 (pages 446-449) Part I
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Part IV For each question, use the
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20 Score Explanation 6 The followin
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17 Score Explanation 4 The followin
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Part II For each question, use the
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Part IV For each question, use the
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Part III For each question, use the
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Chapters 1-9 (pages 461-463) Part I
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19 Score Explanation 6 The followin
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12 Score Explanation 2 31, and an a
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20 Score Explanation 6 The followin
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16 Score Explanation 4 DN √ 106
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20 Score Explanation 2 a 3, and an
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17 Score Explanation 4 6 √ 5 , a
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20 Score Explanation 6 The followin
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16 Score Explanation 4 mADE 93, mB
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20 Score Explanation Chapters 1-14
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Part IV For each question, use the
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Practice Regents Examination One (p
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36 Score Explanation 4 36, and an a
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32 Score Explanation 2 108, and an
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Part II For each question, use the
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Part IV For each question, use the