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.
 
measure_1_1.png
 
Step \(2\): Place a point \(P\) anywhere on the sheet.
 
Fig_9.png
 
Step \(3\): Place the set square on the line such that the arm having \(90^\circ\) lies on the line.
 
Fig_10.png
 
Step \(4\): Place a ruler on the other side of the set square.
 
Fig_11.png
 
Step \(5\): While holding the ruler firmly, slide the set square until the other arm of the set square touches the point \(P\).
 
Fig_12.png
 
Step \(6\): Now draw a line from \(P\) until it meets the line already drawn at \(Q\).
 
Fig_13.png
Construction using rulers and compasses
Step \(1\): Draw a line using a ruler on the sheet of paper.
 
measure_1_1.png
 
Step \(2\): Place a point \(P\) anywhere on the sheet.
 
Fig_9.png
 
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 \(B\).
 
Draw_3.png
 
Step \(4\): With \(A\) as centre, draw an arc anywhere on the sheet of paper.
 
Draw_4.png
 
Step \(5\): With \(B\) as centre, intersect the arc drawn earlier at \(Q\).
 
Draw_5.png
 
Step \(6\): Now, join the points \(P\) and \(Q\) to form the line segment perpendicular to \(\overline{\rm AB}\).
 
Draw_6.png
 
From, the figure given above, \(\overline{PQ}\) \(\perp\) \(\overline{AB}\)