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Construct A Perpendicular Line




 

In these lessons, we will learn

  • how to construct a perpendicular to a line, through a point on a line.
  • how to construct a perpendicular to a line, through a point not on a line.
Related Topics: More Geometry Lessons

Construct a perpendicular to a line, through a point on the line

We will now show how to construct a perpendicular to a line segment, through a point on the line. 

Example :

Construct a line perpendicular to PQ through the point R on PQ.


Solution:

Step 1: Stretch your compasses a short length. It can be any length. Put the sharp end of the compasses on point R and mark two arcs S and T on the line PQ.


Step 2: Stretch the compasses a little more. Put the sharp end of the compasses on point S and make an arc with pencil end. Do the same on point T but make sure that the second arc intersects the first arc.

Step3: Draw a line from point R to the point where the arcs intersect. This line is perpendicular to PQ and passes through the point R.




The following video shows how to construct a perpendicular to a line segment, through a point on the line.
How to construct a perpendicular line from a point on a line.


 

Construct a perpendicular to a line, through a point not on the line

We will now construct a perpendicular to a line, through a point not on the line.

Example :

Construct a line perpendicular to the line AB and passing through the point P, that is not on the line,


Solution:

Step 1: Put the sharp end of your compasses on point P, stretch the compasses and mark two arcs R and S on the line AB.


Step2: Without changing the width of the compasses, put the sharp end of the compasses at R and draw an arc on the other side of AB compared with P. Do the same at S and make sure that the second arc intersects the first arc.


Step 3 : Draw a line from P to the point of intersection. This line passes through point P and is perpendicular to AB.



Constructing a perpendicular to a line, through a point not on the line.
How to construct a perpendicular line from a point to a line.


 

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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