Draw a circle with its center on A to find two additional points over the line:
Then, draw two circles with the same radii centered on A' and A'', and label the intersections of those two circles with B and C:
Draw a line through B and C: it is perpendicular to the given line and passes through the point A.
The compass setting should be larger to draw the circles centered at A' and A'' because they would not intersect otherwise, making impossible to find the points B and C.
