Hello there! I have a question for some of the more advanced modelers here. For a number of different reasons throughout my Blender career, I’ve found it necessary to create an arbitrary axis to transform vertices along (which I only just recently learned you can do through the N-key menu in 3D view, under “Transform Orientations”). Using this tool, I also would like to move vertices to specific points through interaction of the arbitrary axes and the global axes (I’ll explain what I mean in a moment!), but I could never find a way! Would anyone be able to help? It’s a bit of a difficult problem to explain verbally (type-ally?), so I made an example below.

Say I have the shape below:

I have a point that, for whatever reason, is perfectly aligned between two others to create a straight edge (the upper right highlighted point). I would like to move it to the same z (vertical) height as the left highlighted point, but I would also like to maintain the perfect edge that it creates with the vertices above and below it. In other words, I want to move the upper right highlighted point along the arbitrary axis defined by the right-most edge of the entire quadrilateral, such that it intersects the y (horizontal) axis at the same z (vertical) height as the left highlighted point. A visual representation of these can be seen in the figure below (the red vertex should move to the intersection of the red and blue dotted lines):

The result of such an operation should create the figure seen below (of course, to create this tutorial, I took these photos in reverse, using the vertex drag [double-tap “g”] tool ):

I don’t know how to achieve this, but I imagine that the solution might involve some combination or permutation of the vertex-drag tool, the knife tool, the transform orientations menu, and scaling-to-zero with respect to the 3D cursor on some axis. The solution may be simple and staring me in the face, but for the life of me I can’t figure it out! Any help would be greatly appreciated.

Edit: I understand that this effect can be achieved APPROXIMATELY (even relatively precisely) by using the vertex-drag tool, however I would like to have an exact solution if possible. Thank you!