Rather than film my own video on the subject, here is one produced by Alvin. It is informative, but a bit of a commercial. I don't recommend the modern Alvin compasses shown, any more than other modern ones. I do recommend an antique Alvin as well as just about any antique made in the USA or Germany.
In the video below there are no spoken words, and the demonstrator shows that the line can start at any position or angle on the paper. The video is by Antonija Horvatek, who taught grade school mathematics in Croatia. Bisecting is a universal language!
Here is another video. The presenter verbally describes every step. I cannot attribute this video to anyone, as no name is shown on Youtube. What I like about it (besides the verbal explanation) is that the presenter does two things that I do not recommend, and you can see the results: one, he scribes his arcs over and over with the compass, making them imprecise; and two, he draws his perpendicular line without carefully lining the pen to the crossing points, making a visibly inaccurate bisector. That is okay in a class that is all theory, but is not okay in a design class.
As a side note, if you were to draw an arc of a given length instead of a straight line, you could use this same method to find its midpoint and perpendicular intersection.
If you have drawn an angle on your paper and need to divide it in two, the procedure is easy with a compass. The video below was made by the same person who made the second one above. This time he hits the marks much more closely. These videos are ancient... they are from 2011!
The video below shows how it is possible to make a perpendicular line at any position you like on a line segment by putting a point on the line. This process is closely related to bisecting. In fact, it is identical to bisecting an angle if the angle was 180°.
The video was created by Antonija, the same person who made the wordless bisecting video. Towards the end, she demonstrates a technique I never saw before by using a point in space that is not on the line at all, and bisects the line through it. I learned something new myself!
