Geometry in 3 Dimensions You can use three coordinates (x, y, z) to locate points in three dimensions.

59. Point P has coordinates ( 6 , − 3 , 9 ) open 6 comma negative 3 comma 9 close  as shown below. Give the coordinates of points A, B, C, D, E, F, and G.

    
    Image Long Description

    Distance in 3 Dimensions In a three-dimensional coordinate system, you can find the distance between two points ( x 1 , y 1 , z 1 ) open , x sub 1 , comma , y sub 1 , comma , z sub 1 , close  and ( x 2 , y 2 , z 2 ) open , x sub 2 , comma , y sub 2 , comma , z sub 2 , close  with this extension of the Distance Formula.

    d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 + ( z 2 − z 1 ) 2 d equals . square root of open . x sub 2 , minus , x sub 1 . close squared . plus . open . y sub 2 , minus , y sub 1 . close squared . plus . open . z sub 2 , minus , z sub 1 . close squared end root

Find the distance between each pair of points to the nearest tenth.

60. P ( 2 , 3 , 4 ) , Q ( − 2 , 4 , 9 ) p open 2 comma 3 comma 4 close comma q open negative 2 comma 4 comma 9 close
61. T ( 0 , 12 , 15 ) , V ( − 8 , 20 , 12 ) t open 0 comma 12 comma 15 close comma v open negative 8 comma 20 comma 12 close

Standardized Test Prep

SAT/ACT

62. A segment has endpoints ( 14 , − 8 ) open 14 comma negative 8 close  and (4, 12). What are the coordinates of its midpoint?
    1. (9, 10)
    2. ( − 5 , 10 ) open negative 5 comma 10 close
    3. ( 5 , − 10 ) open 5 comma negative 10 close
    4. (9, 2)
63. Which of these is the first step in constructing a congruent segment?
    6. Draw a ray.
    7. Find the midpoint.
    8. Label two points.
    9. Measure the segment.

Short Response

64. The midpoint of R S ¯ r s bar  is N ( − 4 , 1 ) . n open negative 4 comma 1 close .  One endpoint is S ( 0 , − 7 ) . s open 0 comma negative 7 close .
    1. What are the coordinates of R?
    2. What is the length of R S ¯ r s bar  to the nearest tenth of a unit?

Mixed Review

See Lesson 1-6.

Use a straightedge and a compass.

65. Draw A B ¯ . eh b bar , .  Construct P Q ¯ p q bar  so that P Q = 2 A B . p q equals 2 eh b .
66. Draw an acute ∠ RTS . angle  Construct the bisector of ∠ RTS . angle

See Lesson 1-4.

Use the diagram below.

67. Name ∠ 1 angle 1  two other ways.
68. If m ∠ PQR = 60 , m angle  what is m ∠ RQS ? m angle

Get Ready! To prepare for Lesson 1-8, do Exercises 69–72.

See p. 826.

Complete each statement. Use the conversion table on page 837.

69. 130  in. = □  ft 130 , in. , equals white square ft
70. 14  yd = □  in. 14 , yd equals white square , in.
71. 27  ft = □  yd 27 , ft equals white square yd
72. 2  mi = □  ft 2 mi equals white square ft

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