LHS CAT4e ISM-02-final

LHS CAT4e ISM-02-final - Chapter 2 GRAPHS AND FUNCTIONS...

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161 Chapter 2 GRAPHS AND FUNCTIONS Section 2.1: Rectangular Coordinates and Graphs Connections (page 190) 1. Answers will vary. 2. Answers will vary. Latitude and longitude values pinpoint distances north or south of the equator and east or west of the prime meridian. Similarly on a Cartesian coordinate system, x - and y -coordinates give distances and directions from the y -axis and x -axis, respectively. Exercises 1. False. (±1, 3) lies in Quadrant II. 2. False. The expression should be () 22 21 xx yy −+ . 3. True. The origin has coordinates ( ) 0,0 . So, the distance from ( ) 0,0 to ( ) , ab is 2 2 (0 )(0 ) da b a b =− + −=+ 4. True. The midpoint has coordinates ( ) 3 34 2 , 2 2 (2 , ). bb aa a b ⎛⎞ +− = ⎜⎟ ⎝⎠ 5. True. When x = 0, y = 2(0) + 4 = 4, so the y -intercept is 4. When y = 0, 0 = 2 x + 4 x = ±2, so the x -intercept is ±2. 6. Answers will vary. 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: ( ) ( ) ( ) 1993,31 , 1995,35 , 1997,37 , 1999,35 , 2001,28 ,(2003,25) 10. Any three of the following: ( ) ( ) ( ) 1997,87.8 , 1998,90.0 , 1999,83.7 , 2000,88.5 , 2001,84.3 11. P (–5, –7), Q (–13, 1) (a) 2 2 ( , ) [ 13 – (–5)] [1– (–7)] 8 8 128 8 2 dPQ + =− + = = (b) The midpoint M of the segment joining points P and Q has coordinates –5 (–13) –7 1 18 6 , 2 2 9, 3 . ++ ⎞⎛ = ⎟⎜ ⎠⎝ =− − 12. P (–4, 3), Q (2, –5) (a) ( , ) [2–(–4)] (–5–3) 6 (–8) 100 10 =+ = = (b) The midpoint M of the segment joining points P and Q has coordinates – 4 2 3 (–5) 2 2 , 2 2 1, 1 . = 13. (8, 2), (3, 5) PQ (a) 2 2 (3–8) (5–2) 53 25 9 34 =− + = (b) The midpoint M of the segment joining points P and Q has coordinates 8325 1 17 , 2 2 = . 14. P (±8, 4), Q (3, ±5) (a) () ( ) 2 2 (, ) 3 – 8 5 4 11 (–9) 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
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162 Chapter 2: Graphs and Functions 15. P (–6, –5), Q (6, 10) (a) 22 ( , ) [6–(–6)] [10–(–5)] 12 15 144 225 369 3 41 dPQ =+ == (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 ++ ⎛⎞ ⎜⎟ ⎝⎠ 16. P (6, –2), Q (4, 6) (a) (4–6) [6–(–2)] (–2) 8 46 4 6 8 21 7 =+= = (b) The midpoint M of the segment joining points P and Q has coordinates () 64 26 1 04 5 , 2 2 2 +− + 17. ( ) 32 , 45, P ( ) 2,– 5 Q (a) (, ) 2–3 2 – 5–4 5 –2 2 –5 5 81 2 5 1 3 3 = (b) The midpoint M of the segment joining points P and Q has coordinates 2 45 ( –5 ) , 4235 35 ,2 2 , . 2 18. ( ) ( ) – 7, 8 3 , 5 7, – 3 PQ (a) [5 7 – (– 7)] (– 3 – 8 3) (6 7) (–9 3) 252 243 495 3 55 + (b) The midpoint M of the segment joining points P and Q has coordinates –7 5783 ( –3 ) 47 73 73 2 7, . 2 19. Label the points A (–6, –4), B (0, –2), and C (–10, 8). Use the distance formula to find the length of each side of the triangle. [0–(–6)] [–2–(–4)] 62 3 64 4 0 dAB = ( , ) (–10 – 0) [8 – (–2)] ( 10) 10 100 100 200 dBC =− + = + = [–10–(–6)] [8–(–4)] (– 4) 12 16 144 160 dAC = + = Since ( ) ( ) ( ) 2 40 160 200 , += triangle ABC is a right triangle.
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LHS CAT4e ISM-02-final - Chapter 2 GRAPHS AND FUNCTIONS...

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