How to Construct a Perpendicular Line through a Point on the Line

Greetings math peeps and welcome to another week of MathSux! In this post, we will learn how to construct a perpendicular line through a point on the line step by step. In the past, we learned how to construct a perpendicular bisector right down the middle of the line, but in this case we will learn how to create a perpendicular line through a given point on the line (which is not always in the middle). Following along with the GIF or check out the vide below. Thanks for stopping by and happy calculating! πŸ™‚

What are Perpendicular Lines ?

  • Lines that intersect to create four 90ΒΊ angles about the two lines.
How to Construct a Perpendicular Line through a Point on the Line

What is happening in this GIF?

Step 1: First, we are going to gather materials, for this construction we will need a compass, straight edge, and markers.

Step 2: Notice that we need to make a perpendicular line going through point B that is given on our line.

Step 3: Open up our compass to any distance (something preferably short though to fit around our point and on the line).

Step 4: Place the compass end-point on Point B, and draw a semi-circle around our point, making sure to intersect the given line.

Step 5: Open up the compass (any size) and take the point of the compass to the intersection of our semi-circle and given line.  Then swing our compass above the line.

Step 6: Keeping that same length of the compass, go to the other side of our point, where the given line and semi-circle connect.  Swing the compass above the line so it intersects with the arc we made in the previous step.

Step 7: Mark the point of intersection created by these two intersecting arcs we just made and draw a perpendicular line going through Point B!

Still got questions? No problem! Don’t hesitate to comment with any questions below or check out the video above. Thanks for stopping by and happy calculating! πŸ™‚

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Want to see how to construct a square inscribed in a circle? Or maybe you want to construct an equilateral triangle? Click on each link to view each construction!

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