This demonstration shows how to draw a
perpendicular to a line through
an external point using
only a compass and straight edge. See "Introduction to Euclidean Constructions"
We start with a line and an external point R.
The result is a perpendicular line passing through R and intersecting the first line at J.
Instructions Click on 'Next' to go through the construction one step at a time, or click on 'Run' to let it run without stopping.
(If there is no image below, see support page.)
The animated diagram above shows how to construct a
perpendicular
through a point using just a compass and straightedge.
Note that the straight edge can be a ruler, but it is not used to actually measure anything, just to draw straight lines.
Step-by-step Instructions
| Step 1 |
Place the compass on the given external point R. |
| Step 2 |
Set the compass width to a approximately 50% more than the distance to the line. The actual width does not matter. |
| Step 3 |
Draw an arc across the line on each side of R, making sure not to adjust the compass width in between. |
| Step 4 |
At this point, you can adjust the compass width. Recommended: leave it as is.
From each point P,Q, draw an arc below the line so that the arcs cross. |
| Step 5 |
Align a straightedge between R and the point where the arcs intersect.
Draw the perpendicular line from R to the line, or beyond if you wish. |
| Step 6 |
Done. This line is perpendicular to the first line and passes through the point R |
Try it yourself
Click here for a printable construction worksheet containing two 'perpendiculars through a point' problems to try.
When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
Other constructions
Lines
Angles
Triangles
Triangle Centers
Circles, Arcs and Ellipses
Non-Euclidean constructions
(C) 2007 Copyright John Page