Add new vertex to existing edge

Hi Roxana,

 What I usually do,  is selecting the Edge and then Subdivide it.

But, with your method, you most likely won't hit the Edge exactly, so you'd have to Snap the new Vertex to the Edge and also have Auto Merge and Split Edges and Faces enabled:

Yes it's better if you subdivide. If you want to try the control plus click, if you don't want to have a vertex floating by it's own, you can select a vertex and then with the vertex select do the control click and the vertex you add will be connected by an edge, so it's basically an extrusion. 

First time I've seen split edges and faces. That works nice Mister Wizard. Just tried it right now.