Solutions for College Algebra And Trigonometry 6th Us Edition by Lial

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Chapter 2 GRAPHS AND FUNCTIONS Section 2.1 Rectangular Coordinates and Graphs

8. True

1. The point (–1, 3) lies in quadrant II in the rectangular coordinate system.

2. The point (4, 6) lies on the graph of the equation y = 3x – 6. Find the y-value by letting x = 4 and solving for y. y  3  4  6  12  6  6 3. Any point that lies on the x-axis has y-coordinate equal to 0.

5. The x-intercept of the graph of 2x + 5y = 10 is (5, 0). Find the x-intercept by letting y = 0 and solving for x. 2 x  5 0  10  2 x  10  x  5 6. The distance from the origin to the point (–3, 4) is 5. Using the distance formula, we have d ( P, Q)  (3  0) 2  (4  0) 2

7. True

32  42  9  16 

10. False. The distance between the point (0, 0) and (4, 4) is d ( P, Q)  (4  0) 2  (4  0) 2  42  42  16  16  32  4 2

4. The y-intercept of the graph of y = –2x + 6 is (0, 6).



9. False. The midpoint of the segment joining (0, 0) and (4, 4) is 40 40 4 4 ,     ,    2, 2 . 2 2  2 2

25  5

11. Any three of the following: 2, 5 , 1, 7  , 3, 9 , 5, 17  , 6, 21 12. Any three of the following: 3, 3 , 5, 21 , 8,18 , 4, 6 , 0, 6 13. Any three of the following: (1999, 35), (2001, 29), (2003, 22), (2005, 23), (2007, 20), (2009, 20) 14. Any three of the following: 2002,86.8 , 2004, 89.8 , 2006, 90.7 , 2008, 97.4 , 2010, 106.5 , 2012,111.4 , 2014, 111.5 15. P(–5, –6), Q(7, –1) (a) d ( P, Q)  [7 – (–5)]2  [1 – (–6)]2  122  52  169  13

(b) The midpoint M of the segment joining points P and Q has coordinates  –5  7 6  (1)   2 7  ,     ,   2 2 2 2 7   1,   .  2

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