Answer:
see attached
Explanation:
You want a perpendicular to the line at point P.
Procedure
You know how to construct a perpendicular bisector, so you do that—after you have created a segment with P as its midpoint.
To put P at the midpoint of a segment, set your compass to a length slightly less than the shortest part of the line segment from P. Use that radius to draw an arc (red) on the line on either side of P. Now P is the midpoint of those points of intersection (E and F in the attachment).
Perpendicular bisector
Now, increase the radius of your compass by some amount. It is convenient for it to be about half again what it was.
Using this setting and points E and F as centers, draw arcs (green) either side of the line so they intersect at points K and L.
The line KL is perpendicular to the given line at point P.
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Additional comment
You don't need the whole circle or the continuous arc. You only need a short arc through the point of intersection.
We draw points K and L so there is a longer distance between the points defining the perpendicular line. This can help make it more accurately perpendicular.
It is important to keep the same radius for the arcs centered at E and F. That is what ensures K and L are equidistant from both E and F, which they must be if KL is to bisect EF. You can use this procedure to draw the perpendicular bisector of any segment EF. (It works well to make radius EK about 3/4 of the distance EF.)
You actually only need K or L for this problem, because you know point P is also on the perpendicular line.
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