C Challenge

Do the three points lie on one line? Justify your answer.

58. (5, 6), (3, 2), (6, 8)
59. ( − 2 , − 2 ) , ( 4 , − 4 ) , ( 0 , 0 ) open negative 2 comma negative 2 close comma open 4 comma negative 4 close comma open 0 comma 0 close
60. ( 5 , − 4 ) , ( 2 , 3 ) , ( − 1 , 10 ) open 5 comma negative 4 close comma open 2 comma 3 close comma open negative 1 comma 10 close

Find the value of a such that the graph of the equation has the given slope.

61. y = 2 9 a x + 6 ; m = 2 y equals , 2 ninths , eh x , plus 6 , semicolon , m equals 2
62. y = − 3 a x − 4 ; m = 1 2 y equals , minus 3 eh x minus 4 semicolon , m equals , 1 half
63. y = − 4 a x − 10 ; m = − 2 3 y equals , minus 4 eh x minus 10 semicolon , m equals . negative , 2 thirds

Standardized Test Prep

SAT/ACT

64. A B ¯ eh b bar has endpoints A(8, k) and B ( 7 , − 3 ) . b open 7 comma negative 3 close .  The slope of A B ¯ eh b bar is 5. What is k?
    1. 1
    2. 2
    3. 5
    4. 8
65. Two angles of a triangle measure 68 and 54. What is the measure of the third angle?
    6. 14
    7. 58
    8. 122
    9. 180

66. Which of the following CANNOT be true?

    

    1. plane  A B C D ||  plane  E F G H plane eh b c d vertical linevertical line , plane e f g h
    2. Planes ABCD and CDHG intersect in C D ↔ . modified c d with left right arrow above , .
    3. ABCD and ABC represent the same plane.
    4. plane  A D H E ||  plane  D C G plane eh d h e vertical linevertical line , plane d c g
67. The length of a rectangle is ( x − 2 ) open x minus 2 close  inches and the width is 5x inches. Which expression represents the perimeter of the rectangle in inches?
    6. 6 x − 2 6 x minus 2
    7. 12 x − 4 12 x minus 4
    8. 5 x 2 − 10 x 5 , x squared , minus 10 x
    9. 10 x 2 − 20 x 10 , x squared , minus 20 x

Short Response

68. One of the angles in a certain linear pair is acute. Your friend says the other angle must be obtuse. Is your friend's conjecture reasonable? Explain.

Mixed Review

See Lesson 3-6.

For Exercises 69 and 70, construct the geometric figure.

69. a rectangle with a length twice its width
70. a square

See Lesson 2-5.

Name the property that justifies each statement.

71. 4 ( 2 a − 3 ) = 8 a − 12 4 open 2 eh minus 3 close . equals 8 eh minus 12
72. If b + c = 7 b plus . c equals 7  and b = 2 , b equals 2 comma  then 2 + c = 7 . 2 plus . c equals 7 .
73. R S ¯ ≅ R S ¯ r s bar , approximately equal to , r s bar
74. If ∠ 1 ≅ ∠ 4 , angle 1 approximately equal to angle 4 comma  then ∠ 4 ≅ ∠ 1 . angle 4 approximately equal to angle 1 .

Get Ready! To prepare for Lesson 3-8, do Exercises 75–77.

See Lesson 3-7.

Find the slope of the line passing through the given points.

75. ( 2 , 5 ) , ( − 2 , 3 ) open 2 comma 5 close comma open negative 2 comma 3 close
76. ( 0 , − 5 ) , ( 2 , 0 ) open 0 comma negative 5 close comma open 2 comma 0 close
77. ( 1 , 1 ) , ( 2 , − 4 ) open 1 comma 1 close comma open 2 comma negative 4 close

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