Question

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

Answer 1

Steps of construction:

(i) Draw a line segment $\overline{AB}$ of any length and mark a point M on it.
(ii) With M as centre and a convenient radius, draw an arc intersecting the line AB at two points C and B.
(iii) With C and D as centres and a radius greater than MC, draw two arcs, which cut each other at P.
(iv) Join PM. Then PM is perpendicular to AB through the point M.