### Theory:

A perpendicular to a line can also be drawn without a point on it.

Let us look at how to do that.
Construction using rulers and set squares
Step $$1$$: Draw a line using a ruler on the sheet of paper.

Step $$2$$: Place a point $$P$$ anywhere on the sheet.

Step $$3$$: Place the set square on the line such that the arm having $$90^\circ$$ lies on the line.

Step $$4$$: Place a ruler on the other side of the set square.

Step $$5$$: While holding the ruler firmly, slide the set square until the other arm of the set square touches the point $$P$$.

Step $$6$$: Now draw a line from $$P$$ until it meets the line already drawn at $$Q$$.

Construction using rulers and compasses
Step $$1$$: Draw a line using a ruler on the sheet of paper.

Step $$2$$: Place a point $$P$$ anywhere on the sheet.

Step $$3$$: With $$P$$ as centre and with any radius, draw an arc such that the arc intersects the line at two points $$A$$ and $$B$$.

Step $$4$$: With $$A$$ as centre, draw an arc anywhere on the sheet of paper.

Step $$5$$: With $$B$$ as centre, intersect the arc drawn earlier at $$Q$$.

Step $$6$$: Now, join the points $$P$$ and $$Q$$ to form the line segment perpendicular to $$\overline{\rm AB}$$.

From, the figure given above, $$\overline{PQ}$$ $$\perp$$ $$\overline{AB}$$