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hendricks_intermediate_algebra_1e_ch1_3

Section 3.1 The Coordinate System, Graphing Equations, and the Midpoint Formula 155 Student Check 4 The graph of y = |x| - 3 is provided. Use the graph to determine if the given ordered pair is a solution of y = |x| - 3. a. (3, 0) b. (0, 3) c. (0, -3) d. (4, -1) e. (-4, 1) 2 2 4 4 –2 –4 –2 –4 x y The Midpoint Formula The midpoint of a line segment is the ordered pair that lies exactly in the middle of the line segment. For example, the midpoint of 4 and 6 is 5 since 5 lies exactly in the middle of 4 and 6. We can also obtain the midpoint of 4 and 6 with the following calculation. Recall the midpoint of two numbers on a real number line is the average of the two numbers. t 0 1 2 3 4 5 6 7 8 9 10 4 + 6 2 = 10 2 = 5 We can extend this concept to finding the midpoint of a line segment formed by two ordered pairs. We find the average of the x-coordinates and the average of the y-coordinates to determine the midpoint. Consider the line segment formed by (0, 4) and (2, 0). The average of the x-values is 0 + 2 2 = 2 2 = 1. The average of the y-values is 4 + 0 2 = 4 2 = 2. So, the midpoint of the line segment is (1, 2). We can state the midpoint formula as follows. Property: Midpoint Formula If (x1, y1) and (x2, y2) are ordered pairs, then the midpoint of the line segment formed by these ordered pairs is given by Midpoint = a x1 + x2 2 , y1 + y2 2 b 6 t Procedure: Finding the Midpoint of a Line Segment Given Two Ordered Pairs Step 1: Label the ordered pairs as (x1, y1) and (x2, y2). Step 2: Substitute the appropriate values into the midpoint formula and simplify. Objective 5 Examples Find the midpoint of the line segment formed by the ordered pairs. 5a. (4, -1) and (-6, 5) 5b. a1 2 , -3b and a7 3 , 4b Objective 5 ▶ Determine the midpoint of a line segment. 2 2 4 4 6 –2 –4 –2 –4 x y (0 4) (1 2) (2 0) t x y (x1 y1) (x2 y2)


hendricks_intermediate_algebra_1e_ch1_3
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