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3.10: Perpendicular Lines in the Coordinate Plane

  • Page ID
    4772
  • Lines with opposite sign, reciprocal slopes that intersect at right angles.

    Here you'll learn that the slopes of perpendicular lines are negative reciprocals of each other. You'll then apply this fact to determine if two lines are perpendicular and to find what their equations are.

    Perpendicular lines are two lines that intersect at a , or right, angle. In the coordinate plane, that would look like this:

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    Figure \(\PageIndex{1}\)

    If we take a closer look at these two lines, the slope of one is -4 and the other is .

    This can be generalized to any pair of perpendicular lines in the coordinate plane. The slopes of perpendicular lines are opposite reciprocals of each other.

    What if you were given two perpendicular lines in the coordinate plane? What could you say about their slopes?

    Vocabulary

    Term Definition
    perpendicular Two lines that intersect at a \(90^{\circ}\), or right, angle. The slopes of perpendicular lines are opposite reciprocals of each other.

    Additional Resource

    Interactive Element

    Video: Equations of Parallel and Perpendicular Lines

    Activities: Perpendicular Lines in the Coordinate Plane Discussion Questions

    Study Aids: Lines in the Coordinate Plane

    Practice: Perpendicular Lines in the Coordinate Plane

    Real World: Perpendicular Lines In The Coordiante Plane