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Pre-Calculus Homework Solutions 7

# Pre-Calculus Homework Solutions 7 - 2 3 45 S 5 3 3 5 3 10 3...

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Unformatted text preview: 2 3 45. S 5 , 3 3 5 3 10 3 8 3 ¬ x2 2 2 3 , 5 2 x2 5 3 x2 ¬ 6 2 ¬2 3 52. The new coordinates are A (3, 9), B (18, 30), and C (33, 54). d ¬ (x2 x1)2 (y2 y1)2 A B ¬ (18 3)2 (30 9)2 A B ¬ 152 212 225 441 A B ¬ 666 B C ¬ (33 18)2 (54 30)2 B C ¬ 152 242 225 576 B C ¬ 801 A C ¬ (33 3)2 (54 9)2 A C ¬ 302 452 900 2025 A C ¬ 2925 The perimeter of A B C is 666 801 2925, which is approximately 108.2 units. 53. Sample answer: The perimeter increases by the same factor. y2 y2 ¬5 2 y2 ¬x2 11 ¬y2 8 The coordinates of T are 3 , 11 . x1 46. M(31.1, 99.3) x1 31.1 ¬ 62.2 ¬x1 30.4 106.4 2 31.8 y1 , 2 31.8 2 99.3 ¬x1 31.8 ¬ y1 198.6 ¬y1 92.2 106.4 2 ¬y1 106.4 The other endpoint is at (30.4°, 92.2°). 47. LaFayette, LA is near (30.4°, 92.2°). 48. Sample answer: SQRT((A2 C2) 2 (B2 D2) 2) 49a. (54 113)2 (120 215)2 111.8 49b. (68 175)2 (153 336)2 212.0 49c. (421 502)2 (454 798)2 353.4 49d. (837 612)2 (980 625)2 420.3 49e. (1967 1998)2 (3 24)2 37.4 49f. (4173.5 2080.6)2 (34.9 22.4)2 2092.9 50. d ¬ (x2 x1)2 (y2 54a. F x2 y1 , 2 y2 2 F 2 2 6, 6 2 6 F 8 , 12 or F(4, 6) 22 E x1 x2 y1 2 , y2 2 E 6 2 6, 6 2 2 E 12 , 8 or E(6, 4) 22 54b. G(4, 4); it has the same x-coordinate as F and the same y-coordinate as E. 54c. DG GB; use the Distance Formula to show DG GB. d ¬ (x2 x1)2 (y2 y1)2 y1)2 1)2 AB ¬ (6 (10 3)2 2 2 AB ¬ 5 7 25 49 AB ¬ 74 BC ¬ (11 6)2 (18 10)2 BC ¬ 52 82 25 64 BC ¬ 89 AC ¬ (11 1)2 (18 3)2 AC ¬ 102 152 100 225 AC ¬ 325 The perimeter of ABC is 74 89 325, which is approximately 36.1 units. 51. The new coordinates are A (2, 6), B (12, 20), C (22, 36). d ¬ (x2 x1)2 (y2 y1)2 2)2 x1 DG ¬ (4 2)2 DG ¬ 22 22 DG ¬ 8 GB ¬ (6 4)2 GB ¬ 22 22 GB ¬ 8 Thus, DG GB. 55. 1 (x2 4 1 4 (y2 6)2 A B ¬ (12 (20 A B ¬ 102 142 100 196 A B ¬ 296 B C ¬ (22 12)2 (36 20)2 B C ¬ 102 162 100 256 B C ¬ 356 A C ¬ (22 2)2 (36 6)2 A C ¬ 202 302 400 900 A C ¬ 1300 The perimeter of A B C is 296 356 1300, which is approximately 72.1 units. x1) y1) (4 2)2 44 (6 4)2 44 1 4 [5 ( 3)] 1 4 (8) 2 1 4 [12 ( 8)] 1 4 (20) 5 ( 3 2, 8 5) ( 1, 3) Verify that the coordinates of X are ( 1, WX [ 1 ( 3)]2 [ 3 ( 8)]2 WX 22 52 WX 4 25 WX 29 WZ [5 ( 3)]2 [12 ( 8)]2 WZ 82 202 WZ 64 400 WZ 464 29 5.385 464 21.540 5.385 1 (21.540), so WX 1 WZ. 4 4 9 3): Chapter 1 ...
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