Draw any line segment $\overline{AB}$. Mark any point M on it. Through M, draw a perpendicular to $\overline{AB}$. (use ruler and compasses)

We may draw a perpendicular to AB through M:

Step I: Draw a line segment $\overline{AB}$ and mark a point M on it.
Step II: Put the needle of the compass at M and draw an arc of suitable radius such that it intersects $\overline{AB}$ at C and D.

Step III: Take C and D as centres and radii greater than $\overline{CM}$, draw two arcs such that they intersect each other at P.
Step IV: Join M and P.
Therefore, PM is perpendicular to $\overline{AB}$.