Constructing  perpendiculars

Constructing perpendiculars to a line through a specific given point using only a straightedge and a compass is what I will show you here. There are two cases that you may encounter.

Case #1: You are given a line and a point on the line.

Constructing a perpendicular when point is on the line


Case #2: You are given a line and a point not on the line.

Constructing a perpendicular when point is not on line

We will demonstrate both cases.

Constructing perpendiculars: Let us start with case #1.

Step #1

Start with the following line and point P

Constructing a perpendicular when point is on the line


Open your compass to any radius or distance. Put the needle of the compass at point P and draw arcs on both sides of point P. Label the points where the arcs intersect the line C and D.

Constructing a perpendicular when point is on line: step 1

Step #2

Open your compass to a radius or distance greater than the distance you chose to draw the arcs.

After you have increased your compass opening, place the needle at C and draw and arc.

Then, still using the same compass opening place the needle at D and draw another arc.

The two arcs should intersect as shown below. Call the point the two arcs intersect E.

Constructing a perpendicular when point is on line: step 2


Step #3

Draw a line between P and E and you are done!

Constructing a perpendicular when point is on line: step 3

Constructing perpendiculars: case #2.


Case #2: You are given a line and a point not on the line.

Start with the following line and point P not on the line.

Constructing a perpendicular when point is not on the line

Step #1

Open your compass to a radius or distance greater than the distance from P to the line.

The distance you see below in red is the shortest distance from P to the line. That is what I mean by distance from P to the line; It is the shortest distance from P to the line which is usually done by drawing a straight line down.

Constructing a perpendicular when point is not on the line: step 1

Open you compass to a distance greater than that.

Step #2

After opening your compass to a distance greater than the shortest distance from P to the line, place the needle of the compass at P and draw arcs that intersect the line in two places.

Constructing a perpendicular when point is not on the line: step 2

Call the points the arc intersect the line A and B

Step #3

Keeping the opening of the compass the same, place the needle at A and draw and arc.

Then, place the needle at B and draw an arc. Call the point the two arc intersect E.

Constructing a perpendicular when point is not on the line: step 3

Step #4

Draw a line between point P and point E and you are done!

Constructing a perpendicular when point is not on the line: step 4

Here we go! Make sure you understand each step outlined above and follow them carefully. If you do this, you will have no problems whatsoever constructing perpendiculars.

Recent Articles

  1. Quadratic Formula: Easy To Follow Steps

    Jan 26, 23 11:44 AM

    Quadratic formula
    Learn about the quadratic formula, the discriminant, important definitions related to the formula, and applications.

    Read More

  2. Area Formula - List of Important Formulas

    Jan 25, 23 05:54 AM

    Frequently used area formulas
    What is the area formula for a two-dimensional figure? Here is a list of the ones that you must know!

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes