An object may be redefined using its context menu (3.1.1). This is very useful for subsequent changes of your construction. You can also open the Redefine dialog by double clicking on a dependent object.
In order to place a free point A onto a line h, choose Redefine for the point A and enter Point[h]. To remove the point from this line and make it free again, redefine it to some free coordinates like (3,2).
Another example is the conversion of a line h through two points A and B into a segment: choose Redefine and enter Segment[A, B].
Redefining objects is a very versatile tool to change constructions width hindsight. Please note that this may also change the order of the construction steps in the construction protocol (3.1.6).