156 Chapter 3 Graphs, Relations, and Functions Solutions 5a. Let (x1, y1) = (4, -1) and (x2, y2) = (-6, 5). a x1 + x2 2 , y1 + y2 2 b = a 4 + (-6) 2 , -1 + 5 2 b Substitute the appropriate values in the midpoint formula. = a-2 2 , 4 2 b Add the numerators of each fraction. = (-1, 2) Simplify. So, the midpoint of the line segment formed by (4, -1) and (-6, 5) is (-1, 2). 5b. Let (x1, y1) = a1 2 , -3b and (x2, y2 ) = a7 3 , 4b . a x1 + x2 2 , y1 + y2 2 b = ° 1 2 7 3 2 + , -3 + 4 2 ¢ Substitute the appropriate values in the midpoint formula. = ° 3 6 14 6 2 + , 1 2 ¢ Write equivalent fractions in the x-coordinate and simplify the y-coordinate. = a17 6 · 1 2 , 1 2 b Simplify the x-coordinate. = a17 12 , 1 2 b Simplify. So, the midpoint of the line segment formed by a1 2 , -3b and a7 3 , 4b is a17 12 , 1 2 b. 4 2 2 7 3 4 4 6 –2 –2 –4 6 17 12 Student Check 5 Find the midpoint of the line segment formed by the ordered pairs. a. (-5, -2) and (7, 0) b. a- 1 4 , 1b and a2 3 ,-5b Applications There are many situations where a relationship exists between two quantities. For example, a person’s weight on a specific day can be written as an ordered pair in the form (day, weight). The population of a country for a specific year can be written as an ordered pair in the form (year, population). A tip applied to a meal can be written as an ordered pair in the form (cost of meal, amount of tip). Data that can be represented as an ordered pair is called paired data. When data is provided in tables, bar graphs, or line graphs, we can convert the data to ordered pairs and use them to plot the data. The plot of this data is called a scatter plot or scatter diagram. Scatter plots can be used to look for patterns or trends that occur in paired data. Note: When plotting data points, it is often necessary to determine an appropriate scale for the axes and to use appropriate minimum and maximum values on the axes. Objective 6 Examples Solve each problem using the given information. 6a. The table shows the number of hybrid electric vehicles (HEVs) sold for the years 1999 through 2010. Use the table to answer the questions. (Source: http:// www.afdc.energy.gov/afdc/data/vehicles.html and http://www.hybridcars.com) Objective 6 ▶ Solve application problems. x y 1 2 –3 1 2 2 4 4 –2 –6 –4 –2 –4 x y (–6 5) (–1 2) (4 –1)
hendricks_intermediate_algebra_1e_ch1_3
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