212 CHAPTER 2 Graphs and Functions 45. Show that if M is the midpoint of the line segment with endpoints P1x1, y12 and Q1x2, y22, then d1P, M2 + d1M, Q2 = d1P, Q2 and d1P, M2 = d1M, Q2. 46. Write the distance formula d = 21x2 - x122 + 1y 2 - y122 using a rational exponent. 43. Poverty Level Income Cutoffs The table lists how poverty level income cutoffs (in dollars) for a family of four have changed over time. Use the midpoint formula to approximate the poverty level cutoff in 2016 to the nearest dollar. Year Income (in dollars) 1990 13,359 2000 17,604 2010 22,315 2015 24,257 2017 25,094 Data from U.S. Census Bureau. 44. Public College Enrollment Enrollments in public colleges for recent years are shown in the table. Assuming a linear relationship, estimate the enrollments for (a) 2007 and (b) 2013. Give answers to the nearest tenth of a million. Year Enrollment (in millions) 2004 12.98 2010 15.14 2016 14.58 Data from National Center for Education Statistics. For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 7 and 8. 47. y = 1 2 x - 2 48. y = - 1 2 x + 2 49. 2x + 3y = 5 50. 3x - 2y = 6 51. y = x2 52. y = x2 + 2 53. y = 2x - 3 54. y = 2x - 3 55. y = 0 x - 20 56. y = -0 x + 40 57. y = x3 58. y = -x3 Concept Check Answer the following. 59. If a vertical line is drawn through the point 14, 32, at what point will it intersect the x-axis? 60. If a horizontal line is drawn through the point 14, 32, at what point will it intersect the y-axis? 61. If the point 1a, b2 is in the second quadrant, then in what quadrant is 1a, -b2? 1-a, b2? 1-a, -b2? 1b, a2? 62. Show that the points 1-2, 22, 113, 102, 121, -52, and 16, -132 are the vertices of a rhombus (all sides equal in length). 63. Are the points A11, 12, B15, 22, C13, 42, and D1-1, 32 the vertices of a parallelogram (opposite sides equal in length)? of a rhombus (all sides equal in length)? 64. Find the coordinates of the points that divide the line segment joining 14, 52 and 110, 142 into three equal parts.
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