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Parallel, Perpendicular, or Neither?


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Perpendicular Lines
A Pair of Perpendicular Lines

A Pair of Perpendicular Lines

Jennifer Ledwith

Characteristics of Perpendicular Lines

  • Perpendicular lines cross to form 90° angles at the intersection.
  • The slopes of perpendicular lines are negative reciprocals. To illustrate, the slope of Line F is 2/5. What is the slope of a line perpendicular to Line F? Flip over the slope and change the sign. The slope of the perpendicular line is -5/2.
  • The product of the slopes of perpendicular lines is -1. For example, 2/5 * -5/2 = -1.

Note: Each set of intersecting lines is not a set of perpendicular lines. Right angles must be formed at the intersection.

Examples of Perpendicular Lines

  • The blue stripes on the flag of Norway.
  • The intersecting sides of rectangles and squares.
  • The legs of a right triangle.
  • Equations: y = -3x + 5; y = 1/3x + 5;
  • The result of the slope formula: m = 1/2; m = -2
  • Lines with slopes that are negative reciprocals. Look at the two lines in the picture. Notice that the slope of the upward sloping line is 5, yet the slope of the downward sloping line is -1/5.



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