Question

Draw line AB. Take point M anywhere outside the line. Using a compass and ruler, draw a line MN perpendicular to line AB.

Answer 1

Steps of construction:
1. Draw line AB. Take any point M outside the line.
2. Placing the compass point at point M and using any convenient distance, draw arcs to cut the line AB at two points P and Q.
3. Place the compass point at P and taking a distance greater than half of PQ, draw an arc on the lower side of line AB.
4. Place the compass point at Q and using the same distance, draw an arc to cut the previous arc at N.
5. Draw the line MN.
6. Line MN is perpendicular to line PQ.