Pre-Calculus Homework Solutions 58

Pre-Calculus Homework Solutions 58 - 10. Start at (1, 2)....

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Unformatted text preview: 10. Start at (1, 2). Move up 2 units and then move right 1 unit. Draw the line through this point and (1, 2). Pages 142–144 Practice and Apply 15. m y 16. m P (1, 2) O x 17. m 11. Find the slope of MN. (y2 y1) (x2 x1) 20 ¬1 5 2 ¬ 4 or 1 2 1 Since 2 2 m ¬ 18. m (y2 y1) (x2 x1) 32 ¬ 7 0 or 1 7 (y y1) ¬2 (x2 x1) ¬ 5 (( 3)) 6 2 1 2 ¬ 4 or 2 (y2 y1) ¬ (x2 x1) ¬ 43 32 ¬ 15 or 5 (y y1) ¬2 (x2 x1) ¬ ¬ 1, the slope of the line perpendicular to MN through A(6, 4) is 2. Graph the line. Start at (6, 4). Move up 2 units and then move right 1 unit. Draw the line through this point and (6, 4). 3 4 7 1 ¬4 3 19. slope of PQ slope of UV y 12 ( 2) ( 3) 3 1 ¬ 12 or 4 ¬ 52 36 ¬ 28 or 4 1 The product of the slopes is 4 ( 4) or is perpendicular to UV. 8 4 20. slope of PQ A(6, 4) O 8 12 x slope of UV 12. The hill has an 8% grade, so the road will rise or fall 8 units vertically with every 100 horizontal 2 units traveled. So the slope is either 18 00 25 8 2 or 100 25 . 2 13. Let (x1, y1) (0, 0) and m 25 . Then y2 because the biker is 120 meters below her starting position. 2 25 2 25 x2 1. So, PQ ¬ 0 3 ( 04) 3 ¬4 ¬6 8 ( 3) ( 4) 9 3 ¬ 12 or 4 The slopes are the same, so PQ is parallel to UV. 21. slope of PQ 120 slope of UV ¬2 1 ( 7 10) 1 6 ¬ 12 or 1 0 4 ¬6 2 1 ¬2 (y y1) ¬2 (x2 x1) 1 ¬ x 20 0 0 2 1 ¬ x 20 2 ¬1500 m 1 ¬9 The slopes are not the same, so PQ and UV are 11 not parallel. The product of the slopes is 22 1 or 4 , so PQ and UV are not perpendicular. Therefore, PQ and UV are neither parallel nor perpendicular. 22. slope of PQ 2 1500. So the current If m 25 then x2 position of the biker is represented by (1500, 120) or ( 1500, 120). 14. The distance is the same no matter which coordinates are used for the biker’s current position. d ¬ (x2 x1)2 (y2 y1)2 ¬ (1500 0)2 ( 120 0)2 ¬ 15002 ( 120)2 ¬ 2,264,400 ¬1505 The biker has traveled 1505 meters down the hill. ¬0 1 2 ( 9) 1 slope of UV ¬9 ¬ 2 1 ( 81) ¬ 9 or 9 1 The product of the slopes is is perpendicular to UV. 23. slope of PQ 8 ¬9 1 9 (9) or 1. So, PQ 1 1 7 ¬8 slope of UV ¬ 2 8 ( 16) 7 ¬8 The slopes are the same, so PQ is parallel to UV. Chapter 3 60 ...
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