Knife Tool Making Extra Faces The knife tool is one of the things I use most in blender. I use it to add vertices with out adding a Loop/cut/slide. I recently got a new laptop and installed blender on it, and it creates a random face when using the cut tool. 
Usually this is what I do to adda vertex, as you can see in the picture.

But as you can see instead of only adding a vertex it connects to the corner of the object.
The type of topology you are trying to create isn't supported by Blender.  BMesh stores faces as a continuous loop of edges - branches and multiple loops aren't supported (yet). 

If you try and create it by merging vertices you will find Blender ejects the edge from the face, creating a wire edge.