question_answer

Draw any line segment \[\overline{AB}.\] Mark any point M on it. Though M, draw a perpendicular to \[\overline{AB}.\](use ruler and compasses).

Answer:

To draw a perpendicular to \[\overline{AB}\], we use the following steps:

Step I: Firstly, draw a line segment \[\overline{AB}\] and take any point M on it.

Step II: With M as centre and a convenient radius, construct an arc intersecting the line \[\overline{AB}\]at two points X and Y.

Step III: With X and Y as centres and a radius greater than \[\overline{XM}\] construct two arcs which cut each other at D.

Step IV: Now, join MD. Then, \[\overline{MD}\] is perpendicular to \[\overline{AB}\] and we can write it as \[\overline{MD}\bot \overline{AB}\].