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Pre-Calculus Homework Solutions 129

# Pre-Calculus Homework Solutions 129 - 53 m B m C ¬180 18...

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Unformatted text preview: 53. m B m C ¬180 18 4y 12 ¬180 7y 6 ¬180 7y ¬174 y ¬25 m A ¬2(25) 12 or 62 m B ¬25 18 or 7 m C ¬4(25) 12 or 112 m C m A so 3x 15 ¬4x 7 15 ¬x 7 8 ¬x CB 0, so 4x 7 ¬0 4x ¬ 7 2y mA 12 y x Thus, 7 4 x BF 5x 5x x 3 30 30 30 x DF 7 2 10 1 2 12 2 71 2 3 2 81 4 90 2 BF DF, so BF DF and F is the midpoint of BD. Therefore, EF is a perpendicular bisector of BD. 60. x a 3 0 3 0 y 0 b c ¬a 3 b c ¬3 c D has coordinates D a 3 b , 3 . 61. Label the midpoints of AB, BC, and CA as E, F, and G respectively. Then the coordinates of c c E, F, and G are a , 0 , a 2 b , , and b , 2 22 2 respectively. The slope of AF a c b , and the slope c of AD b , so D is on AF. The slope of BG b 2a and the slope of BD b c 2a , 2c so D is on BG. The slope of CE and the 2b a 2c slope of CD 2b a , so D is on CE. Since D is a c on AF, BG, and CE, it is the intersection point of the three segments. 9 ¬ 3 or 3 D is 9 units down and 3 units to the right from B. The point C that is 9 units down and 3 units to the right from D has coordinates (12 3, 3 9) or (15, 6). Check that CD DB. CD ¬ (15 12)2 ( 6 3)2 ¬ 9 81 ¬ 90 C has coordinates (15, 6). 62. T UV 63. C DG 64. B CF 65. slope X, U Y, V YZ, TV XZ R, D S, G SW, CG RW D, C G, F GH, BF DH of line containing (4, 8) 18 24 3 9 2 Z, TU XY, W, CD RS, H, BC DG, and (2, 1): 9 2 slope of line containing (x, 2) and ( 4, 5): 8 3 or 5 9 52 4x No, AD is not an altitude of ABC because 5 1. 9 ( 3) 90 59. slope of BD 3 71 2 6 10 1 2 3 4x 2 ¬2 9 3(9) ¬ 2( 4 x) 27 ¬8 2x 19 ¬2x 9.5 ¬x 66. true; 2ab ¬2(2)(5) ¬20 67. false; c(b a) ¬6(5 2) ¬6(3) ¬18 6 1 41 2 ¬1 3 EF because 1 ( 3) 3 3 4x Solve for x. Since the lines are perpendicular, 1 ¬2 BD ¬ ¬4 ¬ 3 12 12 9 ¬ 12 ¬ 90 4 57. D is on CB with CD DB and the slope of CD equals the slope of DB. DB ¬ (12 9)2 (3 12)2 ¬ 9 81 ¬ 90 slope of EF 71 2 81 4 ¬9 4 1 ¬2 x 5 ¬4(x 1) ¬4x 4 ¬4 ¬26 3 12 2 90 2 8. 58. slope of BC slope of AD 9 ¬ 90 4 Page 254 Maintain Your Skills slope of DB 10 1 2 ¬9 4 54. Sample answer: The largest corner is opposite the longest side. Answers should include the following. • the Exterior Angle Inequality Theorem • the angle opposite the side that is 51 feet long 55. A; n p 180 m so m n 180 p 56. D; 1 x 2 ¬ 1. 131 Chapter 5 ...
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