Constructing a perpendicular from a line through a point

Constructing a perpendicular from a point Using compass and straightedge or ruler or ruler

- Printable problem worksheet
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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.)

Step-by-step Instructions

	After doing this	Your work should look like this
	Start with a line and point R which is not on that line.
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 exact 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. Label these points P and Q
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	Place 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. It also bisects the segment PQ (divides it into two equal parts)

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.

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Non-Euclidean constructions