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Perpendicular Line and Slopes: Graphing and Applications

Learn how to find the slope of perpendicular lines, graph them, and apply their properties to real-life scenarios.

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Perpendicular Line and Slopes: Graphing and Applications

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  1. Line hpasses through (3, 0) and (7, 6). Graph the line perpendicular to h that passes through the point (2, 5). STEP 1 Find the slope m1of line h through (3, 0) and (7, 6). 3 6 m1 = = = 6 – 0 2 4 7 – 3 EXAMPLE 3 Draw a perpendicular line SOLUTION

  2. STEP 2 Find the slope m2of a line perpendicular to h. Use the fact that the product of the slopes of two perpendicular lines is –1. m2 – 1 = m2 – 2 = Multiply each side by 3 STEP 3 3 2 2 Use the rise and run to graph the line. 3 EXAMPLE 3 Draw a perpendicular line Slopes of perpendicular lines

  3. ANSWER The correct answer is D. EXAMPLE 4 Standardized Test Practice SOLUTION The rate at which the skydiver descended is represented by the slope of the segments. The segments that have the same slope are aand c.

  4. Line npasses through (0, 2) and (6, 5). Line m passes through (2, 4) and (4, 0). Is n m? Explain. 2 – 5 n = 1 – 3 0 – 6 = = 2 – 6 for Examples 3 and 4 GUIDED PRACTICE SOLUTION Find the slope of linenthrough (0, 2) and (6, 5).

  5. 4 4 – 0 – 2 . m = = = – 2 2 – 4 1 – 1 . nm = – 2 = 2 for Examples 3 and 4 GUIDED PRACTICE Find the slope of line mthrough (2, 4) and (4, 0). Find the product. Since the product of the slopes of line n and m is –1. Hence , they are perpendicular to each other.

  6. In Example 4, which parachute is in the air for the longest time? Explain. ANSWER Parachute C is in air for longest times. It in the air approximately 1.25 minutes longer than either a or b. for Examples 3 and 4 GUIDED PRACTICE

  7. ANSWER The x- intercepts represent time of the landing in the situation. b and c are in the air different amounts of time, so we can eliminate choice b. for Examples 3 and 4 GUIDED PRACTICE In Example 4, what do the x-intercepts represent in the situation? How can you use this to eliminate one of the choices?

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