A little bit different from the construction one, in construction two we the segment first. In construction one, the segment AB is given but in second construction we build the segment.
Draw a line which is perpendicular to AB and pass through the point P.
The principal concept to solve the problem is making perpendicular bisector through point P. The problem now is, which vertex on line that we will choose as center of the arc. From point P, make an arc with P as the center. Choose radius as yours such that the arc intersect the line in two points, namely K and L. See figure 1.16.
As the center, make an arc from K and L, which has radius more than a half of ½KL½. The intersection between arc K and arc L is given name Q. Now, we have explain that the points like construction 1 are K and L, and we build that.
Make a line that is connecting P and Q and we get a line PQ that is perpendicular to line AB through point P outside the line of AB.