Question

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

Answer 1

Steps of construction;

Step-1 Draw a given line segment $PQ$ and mark any point $M$ on it.

Step-2 With $M$ as a centre and convenient radius, construct an arc intersecting the line segment $PQ$ at two points $A$and $B$respectively.

Step-3 Now, with $A$ and $B$ as centres and radius greater than $AM$, construct $2$ arcs on other side. Let these arcs intersect each other at $X$.

Step-4 Join $XM$.

Thus, $XM$ is the required perpendicular to $\overline{PQ}$.