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Solution Manual for College Algebra Concepts Through Functions, 3rd Edition

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    Ch. 0 Foundations: A Prelude to Functions 0.1 The Distance and Midpoint Formulas 1 Use the Distance Formula MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Plot the point. 1) (1, 3) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 A) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 B) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 C) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 D) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 Page 1

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    2) ( -4 , 3) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 A) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 B) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 C) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 D) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 Page 2

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    3) (2, -4 ) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 A) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 B) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 C) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 D) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 Page 3

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    4) ( -2 , -4 ) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 A) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 B) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 C) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 D) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 Page 4

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    5) (0, 6) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 A) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 B) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 C) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 D) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 Page 5

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    6) ( -4 , 0) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 A) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 B) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 C) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 D) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 Tell in which quadrant or on what coordinate axis the point lies. 7) (10, 13) A) Quadrant I B) Quadrant II C) Quadrant III D) Quadrant IV 8) ( -6 , 13) A) Quadrant II B) Quadrant I C) Quadrant III D) Quadrant IV 9) ( -18 , -3 ) A) Quadrant III B) Quadrant I C) Quadrant II D) Quadrant IV 10) (6, -12 ) A) Quadrant IV B) Quadrant I C) Quadrant II D) Quadrant III 11) (0, 6 ) A) y - axis B) x - axis C) Quadrant I D) Quadrant II Page 6

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    12) ( -8 , 0) A) x - axis B) y - axis C) Quadrant I D) Quadrant II Find the distance d(P1, P2) between the points P1 and P2. 13) x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 x -6 -4 -2 2 4 6 y 6 4 2 -2 -4 -6 A) 10 B) 2 C) 3 D) 1 14) x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 A) 53 B) 3 5 C) 14 D) 5 15) x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 A) 2 10 B) 32 2 C) 32 D) 8 Page 7

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    16) x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 x -8 -6 -4 -2 2 4 6 8 y 8 6 4 2 -2 -4 -6 -8 A) 2 5 B) 12 3 C) 12 D) 6 17) P1 = ( 1 , 1 ); P2 = ( 1 , -5 ) A) 6 B) 6 C) 7 D) 5 18) P1 = ( -4 , -5 ); P2 = ( -16 , 0 ) A) 13 B) 169 C) 14 D) 26 19) P1 = (0, -2 ); P2 = ( -4 , -2 ) A) 4 B) 2 C) 2 5 D) 16 20) P1 = (0, 0); P2 = ( 9 , 10) A) 181 B) 181 C) 19 D) 19 21) P1 = (1, 2); P2 = ( -3 , -5 ) A) 65 B) 33 C) 28 D) 3 22) P1 = (4, -2 ); P2 = (2, -6 ) A) 2 5 B) 12 3 C) 12 D) 2 23) P1 = ( -5 , -1 ); P2 = (7, -4 ) A) 3 17 B) 135 15 C) 135 D) 15 24) P1 = ( -0.6 , -0.8 ); P2 = ( -2 , 2.2 ) Round to three decimal places, if necessary. A) 3.311 B) 22 C) 10.469 D) 3.411 Decide whether or not the points are the vertices of a right triangle. 25) ( -2 , -9 ), (7, -9 ), (7, -6 ) A) Yes B) No 26) ( 3 , -4 ), ( 5 , 0), ( 7 , -1 ) A) Yes B) No 27) (1, 7), (7, 9), (6, 4) A) No B) Yes 28) (3, 10 ), (9, 12 ), (15, 5 ) A) No B) Yes Page 8

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    Solve the problem. 29) Find all values of k so that the given points are 29 units apart. ( - 5, 5), (k, 0) A) - 3, - 7 B) - 7 C) 3, 7 D) 7 30) Find the area of the right triangle ABC with A = ( - 2, 7), B = (7, - 1), C = (3, 9). A) 29 square units B) 58 square units C) 58 2 square units D) 29 2 square units 31) Find all the points having an x - coordinate of 9 whose distance from the point (3, - 2) is 10. A) (9, 6), (9, - 10) B) (9, 2), (9, - 4) C) (9, - 12), (9, 8) D) (9, 13), (9, - 7) 32) A middle school ʹ s baseball playing field is a square, 80 feet on a side. How far is it directly from home plate to second base (the diagonal of the square)? If necessary, round to the nearest foot. A) 113 feet B) 114 feet C) 112 feet D) 120 feet 33) A motorcycle and a car leave an intersection at the same time. The motorcycle heads north at an average speed of 20 miles per hour, while the car heads east at an average speed of 48 miles per hour. Find an expression for their distance apart in miles at the end of t hours. A) 52t miles B) t 68 miles C) 52 t miles D) 2t 13 miles 34) Find the length of each side of the triangle determined by the three points P1, P2, and P3. State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. P1 = ( - 5, - 4), P2 = ( - 3, 4), P3 = (0, - 1) A) d(P1, P2) = 2 17; d(P2, P3) = 34; d(P1, P3) = 34 both B) d(P1, P2) = 2 17; d(P2, P3) = 34; d(P1, P3) = 34 isosceles triangle C) d(P1, P2) = 2 17; d(P2, P3) = 34; d(P1, P3) = 5 2 right triangle D) d(P1, P2) = 2 17; d(P2, P3) = 34; d(P1, P3) = 5 2 neither 2 Use the Midpoint Formula MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the midpoint of the line segment joining the points P1 and P2. 1) P1 = (1, 7); P2 = (9, 9) A) (5, 8) B) (10, 16) C) ( -8 , -2 ) D) (8, 5) 2) P1 = ( 4 , 8); P2 = ( -8 , -3 ) A) - 2 , 5 2 B) 6 , 11 2 C) 12 , 11 D) -4 , 5 3) P1 = (7, 1); P2 = ( - 16, - 16) A) - 9 2 , - 15 2 B) 23 2 , 17 2 C) - 9, - 15 D) 9, 15 4) P1 = ( -0.2 , -0.4 ); P2 = ( -1.1 , -2.9 ) A) ( -0.65 , -1.65 ) B) ( -1.65 , -0.65 ) C) ( -0.45 , -1.25 ) D) ( -1.25 , -0.45 ) Page 9

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    5) P1 = (x, 6); P2 = (0, 2) A) x 2 , 4 B) x, 8 C) - x 2 , 4 D) x, 4 6) P1 = (3y, 1); P2 = (4y, 2) A) 7y 2 , 3 2 B) 7y, 3 C) y, 1 D) 3y 2 , 7 2 Solve the problem. 7) If ( 5 , 5 ) is the endpoint of a line segment, and ( 7 , 8) is its midpoint, find the other endpoint. A) (9, 11) B) (9, 2 ) C) ( 1 , -1 ) D) (11, 9 ) 8) If (1, -5 ) is the endpoint of a line segment, and (0, -7 ) is its midpoint, find the other endpoint. A) ( -1 , -9 ) B) ( -1 , -3 ) C) (3, -1 ) D) ( -3 , -7 ) 9) If ( -10 , 7 ) is the endpoint of a line segment, and ( -8 , 2 ) is its midpoint, find the other endpoint. A) ( -6 , -3 ) B) ( -6 , 12) C) ( -14 , 17) D) ( -20 , 11) 10) If ( 4 , 5 ) is the endpoint of a line segment, and ( 0 , 6 ) is its midpoint, find the other endpoint. A) ( -4 , 7 ) B) ( -4 , 4 ) C) ( 12 , 3 ) D) (6, -3 ) 11) The medians of a triangle intersect at a point. The distance from the vertex to the point is exactly two - thirds of the distance from the vertex to the midpoint of the opposite side. Find the exact distance of that point from the vertex A(3, 4) of a triangle, given that the other two vertices are at (0, 0) and (8, 0). A) 2 17 3 B) 17 3 C) 2 D) 8 3 0.2 Graphs of Equations in Two Variables; Intercepts; Symmetry 1 Graph Equations by Plotting Points MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether the given point is on the graph of the equation. 1) Equation: y = x4 - x Point: ( -9 , 6558) A) No B) Yes 2) Equation: x2 - y2 = 36 Point: ( 3 2, 3 2) A) No B) Yes Page 10

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    Graph the equation by plotting points. 3) y = x + 6 x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 A) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 B) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 C) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 D) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 Page 11

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    4) y = 2x - 6 x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 A) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 B) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 C) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 D) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 Page 12

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    5) y = x2 - 9 x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 A) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 B) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 C) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 D) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 Page 13

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    6) 5x + 3y = 15 x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 A) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 B) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 C) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 D) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 Page 14

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    7) 4x 2 + 4y = 16 x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 A) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 B) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 C) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 D) x -10 -5 5 10 y 10 5 -5 -10 x -10 -5 5 10 y 10 5 -5 -10 Solve the problem. 8) If (a, 3) is a point on the graph of y = 2x - 5, what is a? A) 4 B) 1 C) - 1 D) - 4 9) If (3, b) is a point on the graph of 3x - 2y = 17, what is b? A) - 4 B) 4 C) 23 3 D) 11 3 Page 15

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