206 CHAPTER 2 Graphs and Functions EXAMPLE 5 Using the Midpoint Formula Use the midpoint formula to do each of the following. (a) Find the coordinates of the midpoint M of the line segment with endpoints 18, -42 and 1-6, 12. (b) Find the coordinates of the other endpoint Q of a line segment with one endpoint P1-6, 122 and midpoint M18, -22. SOLUTION (a) The coordinates of M are found using the midpoint formula. M= a 8 + 1-62 2 , -4 + 1 2 b = a1, - 3 2b Substitute in M= A x1 + x2 2 , y1 + y2 2 B. The coordinates of midpoint M are A1, - 3 2B. (b) Let 1x, y2 represent the coordinates of Q. Use both parts of the midpoint formula. The coordinates of endpoint Q are 122, -162. S Now Try Exercises 15(b) and 35. y + 12 2 = -2 y + 12 = -4 y = -16 x + 1-62 2 = 8 x - 6 = 16 x = 22 Substitute carefully. x-value of P x-value of M y-value of P y-value of M EXAMPLE 6 Applying the Midpoint Formula Figure 8 depicts how a graph might indicate the increase in the sales generated by fast-food restaurants in the United States from $167.7 billion in 2011 to $233.7 billion in 2017. Use the midpoint formula and the two given points to estimate the sales from fast-food restaurants in 2014, and compare it to the actual figure of $195.4 billion. 2017 2011 240 30 60 90 120 150 180 210 167.7 233.7 Sales (in billions of dollars) Year Data from National Restaurant Association. Sales of U.S. Fast Food Figure 8
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