14 The distance from A to B is √ [2 (7) ] 2 (5 1 ) 2 5 2 4 2 41 . The distance from B to C is √ [3 (2) ] 2 (1 5 ) 2 5 2 4 2 41 . The distance from C to D is √ [(2) 3 ] 2 [(3) 1 ] 2 5 2 4 2 41 . The distance from D to A is √ [(7) (2)] 2 [(1 (3)] 2 5 2 4 2 41 . The perimeter of ABCD 41 41 41 41 4 41 . 15 The length of <strong>the</strong> base ___ AC is <strong>the</strong> difference between <strong>the</strong> x-coordinates of A and C; 6 (4) 10. The height is <strong>the</strong> vertical distance from B to ___ AC or <strong>the</strong> difference between <strong>the</strong> y-coordinates; 6 (6) 12. There<strong>for</strong>e, A 1 _ bh 2 1 _ (10)(12) 60. 2 16 Using <strong>the</strong> distance <strong>for</strong>mula, AB BC 13 and CA 10. The perimeter of ABC 13 13 10 36. 17 Isosceles because PA AT 5 18 Scalene because AB √ 53 , CB √ 74 , and AC √ 29 19 Scalene because MA √ 130 , AD √ 26 , and MD √ 104 20 Scalene because WI √ 26 , IT √ 125 , and WT √ 109 21 All three sides measure 2, <strong>the</strong>re<strong>for</strong>e <strong>the</strong> triangle must be equilateral. 22 The radius is <strong>the</strong> distance from <strong>the</strong> center to any point on <strong>the</strong> circle. r √ (4 1 ) 2 (2 2 ) 2 5 Diameter 2(5) 10 23 The two diagonals are congruent because AD CB 2. 24 A B 2 [(1) 3 ] 2 (2 2 ) 2 32 B C 2 (3 1 ) 2 (2 4 ) 2 8 A C 2 [(1) 1 ] 2 [(2) 4 ] 2 40. 32 8 40 or A B 2 B C 2 A C 2 . 6-2 Translations (pages 94–95) 1 (1) (1, 2) 2 (2) (3, 2) 3 (4) T 8, 4 4 (4) 6 5 T 0, 2 6 T 3, 0 7 (4, 1) 8 (3, 7) 9 (2, 4) 10 (4, 3) 11 (4, 2) 12 (2, 2) 13 T 3, 2 14 T 2, 2 15 (3, 0) 16 (7, 3) 17 (4, 7) 18 K(8, 5) → (2, 9), E(10, 3) → (4, 1), N(2, 2) → (8, 6) 19 y 20 D 10 9 8 7 D" 6 5 4 3 W" D' 2 1 W 5 4 3 2 1 1 2 3 4 5 1 2 3 4 W' 5 6 7 8 9 10 E E' E" a D’(1, 2), E’(6, 3), W’(2, 1) b D(0, 6), E(7, 7), W(3, 3) c T 3, 1 A' W' y 10 9 8 7 6 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 S' S(3, 4) H' A" A(0, 1) W" W(1, 2) S" H(5, 1) a W’(2, 0), A’(3, 3), S’(0, 6), H’(2, 3) b W(5, 1), A(4, 2), S(7, 5), H(9, 2) c T 4 , 1 H" x x 6-2 Translations 29
6-3 Line Reflections and Symmetry (pages 100–101) 1 (3) A 2 (3) V 3 (1) only vertical line symmetry 4 (2) 2 5 (3) (4, 7) 6 y-axis 7 both 8 x-axis 9 y-axis 10 P’(1, 8) 6 5 4 3 2 1 2 3 4 y 5 6 7 8 9 10 P(2, 4) 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 10 1 11 P’(3, 7) P(3, 3) P'(3, 7) P'(1, 8) 8 7 6 5 4 3 2 1 y y 2 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 1 12 P’(4, 1) 2 3 4 5 6 7 8 8 7 6 5 4 3 2 1 y y 2 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 P'(4, 1) y 2 P(4, 5) 30 Chapter 6: Trans<strong>for</strong>mations and <strong>the</strong> Coordinate Plane x x x 13 (5, 2) 14 (2, 3) 15 (2, 5) 16 A’(2, 1), B’(3, 4), C’(4, 5) C(4, 5) 8 7 6 5 4 3 2 1 y 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 1 A'(2, 1) 2 C'(4, 5) 3 4 5 6 7 8 B(3, 4) A(2, 1) B'(3, 4) 17 G’(0, 0), H’(4, 3), I’(1, 4), J’(5, 2) 5 I'(–1, 4) 4 H'(–4, 3) 3 I(1, 4) J(–5, 2) 2 1 6 y H(4, 3) J'(5, 2) 6 5 4 3 21G G'1 2 3 4 5 6 1 2 18 A’(3, 3), B’(5, 8), C’(1, 5) y 10 9 8 7 6 B'(5, 8) C'(1, 5 5) 4 3A'(3, 3) B(8, 5) 2 1 6 5 4 3 2 1 1 2 3 4 A(3, 3) 1 2 3 4 C(5, 1) 5 6 7 8 9 10 x y x 19 Q’(2, 4), Z’(3, 4), D’(1, 2) 5 Z'(3, 4) 4 Z(4, 3) 3 Q'(2, 4) 2 1 D'(1, 2) 6 y 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 1 D Q(4, 2) (2, 1) 3 4 y x x x x
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13-2 Arcs and Chords (pages 350-351
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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