Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Find the coordinate of the midpoint of the segment with the given endpoints.

6. 2 and 4
7. − 9 negative 9  and 6
8. 2 and − 5 negative 5
9. − 8 negative 8  and − 12 negative 12

Find the coordinates of the midpoint of H X ¯ . h x bar , .

10. H(0, 0), X(8, 4)
11. H ( − 1 , 3 ) , X ( 7 , − 1 ) h open negative 1 comma 3 close comma x open 7 comma negative 1 close
12. H ( 13 , 8 ) , X ( − 6 , − 6 ) h open 13 comma 8 close comma x open negative 6 comma negative 6 close
13. H ( 7 , 10 ) , X ( 5 , − 8 ) h open 7 comma 10 close comma x open 5 comma negative 8 close
14. H ( − 6 . 3 , 5 . 2 ) , X ( 1 . 8 , − 1 ) h open negative 6 . 3 comma 5 . 2 close comma x open 1 . 8 comma negative 1 close
15. H ( 5 1 2 , − 4 3 4 ) , X ( 2 1 4 , − 1 1 4 ) h . open . 5 , and 1 half , comma negative 4 , and 3 fourths . close . comma . x . open . 2 , and 1 fourth , comma negative 1 , and 1 fourth . close

See Problem 2.

The coordinates of point T are given. The midpoint of S T ¯ s t bar  is ( 5 , − 8 ) . open 5 comma negative 8 close .  Find the coordinates of point S.

16. T(0, 4)
17. T ( 5 , − 15 ) t open 5 comma negative 15 close
18. T(10, 18)
19. T ( − 2 , 8 ) t open negative 2 comma 8 close
20. T(1, 12)
21. T ( 4.5 , − 2.5 ) t open 4.5 comma negative 2.5 close

See Problem 3.

Find the distance between each pair of points. If necessary, round to the nearest tenth.

22. J ( 2 , − 1 ) , K ( 2 , 5 ) j open 2 comma negative 1 close comma k open 2 comma 5 close
23. L ( 10 , 14 ) , M ( − 8 , 14 ) l open 10 comma 14 close comma m open negative 8 comma 14 close
24. N ( − 1 , − 11 ) , P ( − 1 , − 3 ) n open negative 1 comma negative 11 close comma p open negative 1 comma negative 3 close
25. A(0, 3), B(0, 12)
26. C ( 12 , 6 ) , D ( − 8 , 18 ) c open 12 comma 6 close comma d open negative 8 comma 18 close
27. E ( 6 , − 2 ) , F ( − 2 , 4 ) e open 6 comma negative 2 close comma f open negative 2 comma 4 close
28. Q ( 12 , − 12 ) , T ( 5 , 12 ) q open 12 comma negative 12 close comma t open 5 comma 12 close
29. R(0, 5), S(12, 3)
30. X ( − 3 , − 4 ) , Y ( 5 , 5 ) x open negative 3 comma negative 4 close comma y open 5 comma 5 close

See Problem 4.

Maps For Exercises 31–35, use the map below. Find the distance between the cities to the nearest tenth.

31. Augusta and Brookline
32. Brookline and Charleston
33. Brookline and Davenport
34. Everett and Fairfield
35. List the cities in the order of least to greatest distance from Augusta.

B Apply

Find (a) PQ to the nearest tenth and (b) the coordinates of the midpoint of P Q ¯ . p q bar , .

36. P(3, 2), Q(6, 6)
37. P ( 0 , − 2 ) , Q ( 3 , 3 ) p open 0 comma negative 2 close comma q open 3 comma 3 close
38. P ( − 4 , − 2 ) , Q ( 1 , 3 ) p open negative 4 comma negative 2 close comma q open 1 comma 3 close
39. P ( − 5 , 2 ) , Q ( 0 , 4 ) p open negative 5 comma 2 close comma q open 0 comma 4 close
40. P ( − 3 , − 1 ) , Q ( 5 , − 7 ) p open negative 3 comma negative 1 close comma q open 5 comma negative 7 close
41. P ( − 5 , − 3 ) , Q ( − 3 , − 5 ) p open negative 5 comma negative 3 close comma q open negative 3 comma negative 5 close
42. P ( − 4 , − 5 ) , Q ( − 1 , 1 ) p open negative 4 comma negative 5 close comma q open negative 1 comma 1 close
43. P ( 2 , 3 ) , Q ( 4 , − 2 ) p open 2 comma 3 close comma q open 4 comma negative 2 close
44. P(4, 2), Q(3, 0)
45. Think About a Plan An airplane at T(80, 20) needs to fly to both U(20, 60) and V(110, 85). What is the shortest possible distance for the trip? Explain.
    • What type of information do you need to find the shortest distance?
    • How can you use a diagram to help you?

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