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 the center and a convenient radius, draw an arc intersecting the line $AB$ at two points $C$ and $B.$
(iii) With $C$ and $D$ as center 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 point $M.$