Parallel and perpendicular lines in linear functions

Get the most by viewing this topic in your current grade. Pick your course now.

Introduction
Lessons
    • Definition of Parallel and Perpendicular Lines
    • How does that relate to slope?
Examples
Lessons
  1. Determine whether the three points A (-2,-1), B(0,4) & C(2,9) all lie on the same line.
    1. Determine the following slopes are parallel, perpendicular, or neither.
      i) m1=25,m2=25 m_1 = {2 \over 5}, m_2= {2 \over 5}

      ii) m1=15,m2=51m_1 = {1 \over5} , m_2 = - {5 \over 1}

      iii) m1=47,m2=1221m_1 = {4 \over 7}, m_2 = {12 \over 21}

      iv) m1=m_1 = undefined, m2=0 m_2 = 0

      v) m1=mn1;m2=m1bm_1 =mn^{-1}; m_2 =-m^{-1}b
      1. Given the points of two lines, determine when the lines are parallel, perpendicular or neither.
        1. Line 1: (3,2) & (1,4); Line 2: (-1,-2) & (-3,-4)
        2. Line 1: (5,6) & (7,8); Line 2: (-5,-6) & (-7,-8)
        3. Line 1: (0,4) & (-1,2); Line 2: (-3,5) & (1,7)
      2. Show that the points A(-3,0), B(1,2) and C(3,-2) are the vertices of a right triangle.
        1. Show that the points A(-1,-1), B(3,0), C(2,4) and D(-2,3) are the vertices of a square.
          Free to Join!
          StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.
          • Easily See Your Progress

            We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.
          • Make Use of Our Learning Aids

            Last Viewed
            Practice Accuracy
            Suggested Tasks

            Get quick access to the topic you're currently learning.

            See how well your practice sessions are going over time.

            Stay on track with our daily recommendations.

          • Earn Achievements as You Learn

            Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.
          • Create and Customize Your Avatar

            Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
          Topic Notes
          Parallel lines are lines with identical slope. In other words, these lines will never cross each other. Perpendicular lines will always pass through each other and form right angles at the interception. In this lesson, we will learn how to use information such as, points in lines and their slopes, to determine whether the lines are parallel, perpendicular or neither.
          Parallel
          lines
          - identical slope so they never intersect each other, unless overlapped.

          Perpendicular
          lines
          - two lines form right angles to each other when they intersect. If the slope of first line is ab {a \over b} , the slope of perpendicular line is the slope of perpendicular line is ba - {b \over a} . The product of the two slopes is -1.