The Distance and Midpoint Formulas

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Presentation transcript:

The Distance and Midpoint Formulas ALGEBRA 1 LESSON 11-3 pages 594–597 Exercises 1. 15 2. 14 3. 10 4. 11.3 5. 2.8 6. 8.1 7. 16 8. 21.6 9. (1, 6) 10. (–1, 12) 11. (0, 0) 22. MN 5.1; NP 3.6; MP = 5 23. JK = 4; KL 2.2; LJ 3.6 24. TU 7.6; UV 16.5; VT 13.3 25. a. OR = 29, ST = 29 b. ; c. yes 26. a. (20, 80), (–40, 30) b. 78.1 ft c. (–10, 55) or 55L10 12. (–2, 3) 13. 5, –5 14. – 2 , –1 15. (–4, 4) 16. 8 , –9 17. 10.6 18. 9.4 19. AB 4.1; BC 3.2; AC = 5 20. DE 6.1; EF 3.6; DF 5.7 21. RS 3.2; ST 5.7; RT 5.1 1 2 1 2 5 2 5 2 1 2 11-3

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. 38.1 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 9 + 16 = 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

The Distance and Midpoint Formulas ALGEBRA 1 LESSON 11-3 33. a. R(–27, –5) b. PR = 13 3.6 RQ = 13 3.6 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 47. 11.7 48. 11.2 49. 10.2 50. 26 51. 3.5 52. 8 53. 4.1 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. 41. 19.1 42. 5 43. 22.9 44. –5 45. 3 46. –8 9 5 7 5 , – 11-3

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