Solution Manual for Essentials of College Algebra 11th Edition by Lial Hornsby Schneider and Daniels

Chapter 2 GRAPHS AND FUNCTIONS Section 2.1 Rectangular Coordinates and Graphs

12. P(–4, 3), Q(2, –5) (a) d ( P, Q ) = [2 – (– 4)]2 + (–5 – 3)2

= 62 + (–8)2 = 100 = 10

1. False. (−1, 3) lies in Quadrant II. 2. False. The expression should be

( x2 − x1 ) + ( y2 − y1 ) 2

2

.

3. True. The origin has coordinates (0, 0) . So, the distance from (0, 0) to (a, b ) is

d = (a − 0) 2 + (b − 0) 2 = a 2 + b 2 4. True. The midpoint has coordinates ⎛ a + 3a b + ( −3b ) ⎞ ⎛ 4a −2b ⎞ ⎜ 2 , ⎟ = ⎜⎝ 2 , 2 ⎟⎠ 2 ⎝ ⎠ = (2a, − b). 5. True. When x = 0, y = 2(0) + 4 = 4, so the y-intercept is 4. When y = 0, 0 = 2x + 4 ⇒ x = −2, so the x-intercept is −2. 6. Answers will vary.

(b) The midpoint M of the segment joining points P and Q has coordinates ⎛ – 4 + 2 3 + (–5) ⎞ ⎛ −2 −2 ⎞ , ⎜⎝ ⎟=⎜ , ⎟ 2 2 ⎠ ⎝ 2 2 ⎠ = (−1, −1) . 13. P(8, 2), Q(3, 5) (a) d ( P, Q ) = (3 – 8)2 + (5 – 2)2

=

= 25 + 9 = 34 (b) The midpoint M of the segment joining points P and Q has coordinates ⎛ 8 + 3 2 + 5 ⎞ ⎛ 11 7 ⎞ , ⎜⎝ ⎟=⎜ , ⎟. 2 2 ⎠ ⎝ 2 2⎠ 14. P (−8, 4), Q (3, −5)

7. Any three of the following: (2, −5) , (−1, 7) , (3, −9) , (5, −17) , (6, −21) 8. Any three of the following: (3, 3) , (−5, −21) , (8,18) , (4, 6) , (0, −6) 9. Any three of the following: (1997, 36), (1999, 35), (2001, 29), (2003, 22), (2005, 23), (2007, 20) 10. Any three of the following: (1998, 90.0) , (2000,88.5) , (2002,86.8) , (2004, 89.8) , (2006, 90.7) , (2008, 97.4) , (2010, 106.5)

(a) d ( P, Q ) = ⎡⎣3 – (−8)⎤⎦ + (−5 − 4) 2

(a) d ( P, Q ) = [−13 – (–5)]2 + [1 – (–7)]2

( − 8 )2 + 8 2

= 128 = 8 2

(b) The midpoint M of the segment joining points P and Q has coordinates ⎛ –5 + (–13) –7 + 1 ⎞ ⎛ −18 −6 ⎞ , , ⎟ ⎜⎝ ⎟=⎜ 2 2 ⎠ ⎝ 2 2 ⎠ = (−9, −3) . 166

2

= 112 + (–9)2 = 121 + 81 = 202 (b) The midpoint M of the segment joining points P and Q has coordinates ⎛ –8 + 3 4 + (–5) ⎞ ⎛ 5 1 ⎞ , ⎜⎝ ⎟ = ⎜− , − ⎟. 2 2 ⎠ ⎝ 2 2⎠ 15. P(–6, –5), Q(6, 10) (a) d ( P, Q ) = [6 – (– 6)]2 + [10 – (–5)]2

= 122 + 152 = 144 + 225 = 369 = 3 41

11. P(–5, –7), Q(–13, 1)

=

(−5)2 + 32

(b) The midpoint M of the segment joining points P and Q has coordinates ⎛ – 6 + 6 –5 + 10 ⎞ ⎛ 0 5 ⎞ ⎛ 5 ⎞ , ⎜⎝ ⎟ = ⎜ , ⎟ = ⎜ 0, ⎟ . 2 2 ⎠ ⎝2 2⎠ ⎝ 2⎠

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