What kind of line is being constructed in the series of diagrams?

Perpendicular

Step-by-step explanation:

In figure (i), with Q as centre and any radius  we make two arcs on the line  (using compass) such that each of the arc is equidistant from Q.

Mark the intersecting points on the line as A and B. (see figure (i) )

Now, take A as centre and open compass more than half of the line i.e,  more than AQ, draw an arc (see figure (ii) ).

With the same radius as in figure (ii) and centre B , draw an arc which intersects the previous arc at point P. (see figure (iii) )

If we draw line from the intersecting point P to the line, we get a perpendicular .

So, second option is correct .