1. The Distance and Midpoint Formulas
ALGEBRA 1 LESSON 11-3
pages 594–597  Exercises
1. 15
2. 14
3. 10
5. 2.8
6. 8.1
7. 16
9. (1, 6)
10. (–1, 12)
11. (0, 0)
22. MN ; NP ; MP = 5
23. JK = 4; KL ; LJ
24. TU ; UV ; VT
25. a. OR = , ST =
b. ;
c. yes
26. a. (20, 80), (–40, 30)
b ft
c. (–10, 55) or 55L10
12. (–2, 3)
13. 5, –5
14. – 2 , –1
15. (–4, 4)
, –9
19. AB ; BC ; AC = 5
20. DE ; EF ; DF
21. RS ; ST ; RT 1 2 1 2 5 2 5 2 1 2
11-3

2. The Distance and Midpoint Formulas
ALGEBRA 1 LESSON 11-3
28. Check students’ work.
29. a.
b. (0, – )
c. one half mile south of the substation
30. about 9.5 km apart
31. a mi
b. 20 mi, 21.2 mi
c. 15 min, 16 min
32. Yes; all sides are congruent.
27. Answers may vary. Sample:
Suppose you have (1, 1) and
(4, –3). To find the distance,
square the difference between
the x-coordinates. Square the
difference between the
y-coordinates. Find the sum
and take the square root,
so = 5. To find the
midpoint, add x-coordinates
together and divide by 2.
Repeat for y-coordinates.
So, 1 2
1 + 4 2 ,
1 – 3 2 5 2 =
, –1
11-3

3. The Distance and Midpoint Formulas
ALGEBRA 1 LESSON 11-3
33. a. R(–27, –5)
b. PR =
RQ =
34. a. about 4.3 mi
b. about 17.4 mi
35. a. M(–0.5, 3); N(5.5, 3)
b. They are equal.
36. (x, y)
37. They are opposites.
38. a. 5 units
b. Answers may vary. Sample:
(5, 0), (0, 5), (–5, 0), (0, –5),
(3, –4), (–3, 4), (–3, –4)
c. circle 4 3
50. 26
52. 8
54. –14, 14
55. –10, 10
56. no solution
57. –5, 5
58. no solution
39. a. y = – x + 1 b.
c. 3
40. Yes; the distance from
each point to the
center is 5.
42. 5
44. –5
45. 3
46. –8 9 5 7 5
, –
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4. The Distance and Midpoint Formulas
ALGEBRA 1 LESSON 11-3
59. – ,
60. k2 + 11k + 24
61. v2 + 2v – 35
62. 2p2 – 17p – 9
63. 8w4 + 19w2 + 11
64. 7t3 + 5t2 + 5t – 2
65. 6c3 – 27c2 + 33c + 24 2 3 2 3
11-3