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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 Fall '10
 Dr.Zhan
 Calculus, PreCalculus, Slope, Harshad number, Trigraph, bf Df

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