How to Construct a Perpendicular Line to a Given Line Through Point on the Line

PDF download Download Article
PDF download Download Article

Perpendicular lines are lines that form right angles. These types of lines are used often in geometry, so it is important to know how to construct them. The simplest way to construct a perpendicular line is to use a protractor. However, you will often be asked to construct a perpendicular line using only a compass and straightedge.

Method 1
Method 1 of 2:

Using a Protractor

PDF download Download Article
  1. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/4\/43\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-1-Version-2.jpg\/v4-460px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-1-Version-2.jpg","bigUrl":"\/images\/thumb\/4\/43\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-1-Version-2.jpg\/aid2560782-v4-728px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-1-Version-2.jpg","smallWidth":460,"smallHeight":334,"bigWidth":728,"bigHeight":529,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Set the protractor’s origin hole over the line's given point. Align the protractor so that its base line sits exactly over the given line. [1]
    • The origin hole is the small hole at the bottom-center of the protractor.
    • The base line is the line on the bottom of the protractor marking 180/0 degrees.
  2. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/f\/f7\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-2-Version-2.jpg\/v4-460px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-2-Version-2.jpg","bigUrl":"\/images\/thumb\/f\/f7\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-2-Version-2.jpg\/aid2560782-v4-728px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-2-Version-2.jpg","smallWidth":460,"smallHeight":334,"bigWidth":728,"bigHeight":529,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    This is the line measurement at the very top of the protractor. Two perpendicular lines form a 90-degree, or right, angle. Thus, to draw a perpendicular line, you need to draw a 90-degree angle. [2]
    Advertisement
  3. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/e\/e8\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-3-Version-2.jpg\/v4-460px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-3-Version-2.jpg","bigUrl":"\/images\/thumb\/e\/e8\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-3-Version-2.jpg\/aid2560782-v4-728px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-3-Version-2.jpg","smallWidth":460,"smallHeight":334,"bigWidth":728,"bigHeight":529,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Use the straightedge of the protractor to ensure that the line is straight. This line is perpendicular to the original line, through the given point on the line.
    4. Advertisement
Method 2
Method 2 of 2:

Using a Compass and Straight Edge

PDF download Download Article
  1. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/0\/06\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-4-Version-2.jpg\/v4-460px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-4-Version-2.jpg","bigUrl":"\/images\/thumb\/0\/06\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-4-Version-2.jpg\/aid2560782-v4-728px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-4-Version-2.jpg","smallWidth":460,"smallHeight":334,"bigWidth":728,"bigHeight":529,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    To do this, place the compass tip on the given point on the line. Then, swing the compass, drawing two arcs on both sides of the given point. The arcs should intersect the line. [3] Mark and label the points where the arcs intersect the line.
    • You can set the compass to any width for this step.
    • For example, you might be given point A on a line. Use the compass to draw point P to the left, and point Q to the right.
  2. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/9\/9f\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-5-Version-2.jpg\/v4-460px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-5-Version-2.jpg","bigUrl":"\/images\/thumb\/9\/9f\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-5-Version-2.jpg\/aid2560782-v4-728px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-5-Version-2.jpg","smallWidth":460,"smallHeight":334,"bigWidth":728,"bigHeight":529,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Place the compass tip on the new point to the left of the original point. Stretch the compass so that it reaches about halfway between the original point, and the new point on the right. [4]
    • For example, place the compass tip on point P, and stretch the compass to a point about halfway between points A and Q.
  3. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/f\/f2\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-6-Version-2.jpg\/v4-460px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-6-Version-2.jpg","bigUrl":"\/images\/thumb\/f\/f2\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-6-Version-2.jpg\/aid2560782-v4-728px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-6-Version-2.jpg","smallWidth":460,"smallHeight":334,"bigWidth":728,"bigHeight":529,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    You could also draw the arc below the line. Keeping the compass tip on the left point, swing the compass, drawing an arc. Make sure the arc crosses over the original point. [5]
    • For example, keep the compass tip on point P. Draw an arc above the line.
  4. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/6\/67\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-7.jpg\/v4-460px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-7.jpg","bigUrl":"\/images\/thumb\/6\/67\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-7.jpg\/aid2560782-v4-728px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-7.jpg","smallWidth":460,"smallHeight":334,"bigWidth":728,"bigHeight":529,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Do not change the width of the compass. Set the compass tip on the right point. Swing the compass, drawing an arc above the line that intersects the first arc. [6] Mark this intersection with another point.
    • For example, place the compass tip on point Q. Draw an arc that intersects the first arc at point T.
  5. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/a\/a3\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-8.jpg\/v4-460px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-8.jpg","bigUrl":"\/images\/thumb\/a\/a3\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-8.jpg\/aid2560782-v4-728px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Step-8.jpg","smallWidth":460,"smallHeight":334,"bigWidth":728,"bigHeight":529,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    Use a straightedge to ensure the line is straight. The line you draw is perpendicular to the first line, through the given point on the line. [7]
    • For example, draw a line connecting points A and T.
  6. {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/6\/6f\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Final.jpg\/v4-460px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Final.jpg","bigUrl":"\/images\/thumb\/6\/6f\/Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Final.jpg\/aid2560782-v4-728px-Construct-a-Perpendicular-Line-to-a-Given-Line-Through-Point-on-the-Line-Final.jpg","smallWidth":460,"smallHeight":334,"bigWidth":728,"bigHeight":529,"licensing":"<div class=\"mw-parser-output\"><p>License: <a target=\"_blank\" rel=\"nofollow noreferrer noopener\" class=\"external text\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/3.0\/\">Creative Commons<\/a><br>\n<\/p><p><br \/>\n<\/p><\/div>"}
    7. Advertisement

Community Q&A

Search
Add New Question
  • Question
    Can we draw the arc both above/below the line?
    Donagan
    Top Answerer
    Yes. With either of the methods shown above, you may (but don't have to) draw similar arcs on both sides of the given line. An arc (or arcs) on just one side of the line is sufficient, but drawing them on both sides is a good way to verify the accuracy of the perpendicular line.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 1 Helpful 10
  • Question
    How can I divide a straight line into 6 equal parts?
    Donagan
    Top Answerer
    Assuming no measuring tool or protractor, this can be done with a compass and straightedge. Label the line AB. From A draw another straight line at any acute angle from AB. Mark off six equal segments on this new line. Label the segments AC, CD, DE, EF, FG and GH. Draw a line from H to B. From line AH draw five lines to AB that are each parallel to HB. (Use a compass or protractor to make these lines parallel to HB.) These parallel lines will intersect AB so as to divide AB into six equal parts.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 4 Helpful 7
  • Question
    What if the point is already drawn?
    Donagan
    Top Answerer
    Use that point as "the given point" in either of the above methods.
    Thanks! We're glad this was helpful.
    Thank you for your feedback.
    If wikiHow has helped you, please consider a small contribution to support us in helping more readers like you. We’re committed to providing the world with free how-to resources, and even $1 helps us in our mission. Support wikiHow
    Yes No
    Not Helpful 2 Helpful 4
See more answers
Ask a Question
200 characters left
Include your email address to get a message when this question is answered.
Submit
      Advertisement

      Video

      Tips

      Submit a Tip
      All tip submissions are carefully reviewed before being published
      Submit
      Thanks for submitting a tip for review!

      You Might Also Like

      How to
      Find the Perpendicular Bisector of Two Points
      How to
      Find the Equation of a Line
      How to Calculate the Slope of a Line
      How to
      Construct a Regular Pentagon
      How to
      Construct a 60 Degrees Angle Using Compass and Ruler
      How to
      Construct a 90 Degrees Angle Using Compass and Ruler
      How to
      Construct a 30 Degrees Angle Using Compass and Straightedge
      How to Create a Regular Heptagon
      How to
      Construct a Line Parallel to a Given Line Through a Given Point
      How to
      Bisect a Line With a Compass and Straightedge
      Advertisement

      References

      1. ↑ https://www.math-only-math.com/construction-of-perpendicular-lines-by-using-a-protractor.html
      2. ↑ https://www.math-only-math.com/construction-of-perpendicular-lines-by-using-a-protractor.html
      3. ↑ https://www.mathopenref.com/constperplinepoint.html
      4. ↑ https://www.mathsisfun.com/geometry/construct-perponline.html
      5. ↑ https://www.mathopenref.com/constperplinepoint.html
      6. ↑ https://www.mathsisfun.com/geometry/construct-perponline.html
      7. ↑ https://www.mathopenref.com/constperplinepoint.html

      About This Article

      In other languages
      Thanks to all authors for creating a page that has been read 110,149 times.

      Did this article help you?

      Advertisement