Question

Draw any line segment $AB$. Mark any point $M$ on it. Through $M$, draw a perpendicular using ruler and compass.

Answer 1

Steps of construction:

$\left(i\right)$ With $M$ as centre and a convenient radius, draw an arc intersecting the line $AB$ at two points $C$ and $B$.

$\left(ii\right)$ With $C$ and $D$ as centres and a radius greater than $MC$, draw two arcs, which cut each other at $P$.

$\left(iii\right)$ Join $PM$. Then $PM$ is perpendicular to $AB$ through the point $M$.