Draw a line l and take a point P on it. Through P, draw a line segment $\overline{PQ}$ perpendicular to l. Now draw a perpendicular to $\overline{PQ}$ at Q (use ruler and compass).

Steps:

1. Draw a line l and mark a point P on it.

2. With P as centre and any suitable radius, draw an arc to cut the line l at points C and D.

3. With C and D as centres, draw two arcs of equal radius $\left(\gt\dfrac{1}{2}\text{CD}\right)$ cutting each other at point Q.

4. Join P and Q. Then $\overline{PQ}$ is the required line segment perpendicular to l at point P.

5. Produce PQ beyond Q to form a line PQ'.

6. With Q as centre and any suitable radius, draw an arc to cut the line PQ' at points E and F.

7. With E and F as centres, draw two arcs of equal radius on both side $\left(\gt\dfrac{1}{2}\text{EF}\right)$ cutting each other at point R and S.

8. Draw a line passing through points S,Q and R.

Hence, RS is the required perpendicular to PQ at point Q.