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This question already has an answer here:

I want to ask if that possible to extrude a vertices and connect it in a middle of a plane ?? And If that possible how to do it ? it's my first question and i hope i can find the answer here :D Thanks .. enter image description here

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marked as duplicate by cegaton, VRM, Denis, batFINGER, David Sep 26 '17 at 12:00

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ Could you show some screenshots of what you want to achieve? $\endgroup$ – cgslav Sep 24 '17 at 18:08
  • $\begingroup$ It is nice you have added a picture but now I am even more confused about what do you want to do. What does A and B mean? What does the selected face mean? And there is the plane you are talking about? $\endgroup$ – Jan Kadeřábek Sep 24 '17 at 23:12
  • $\begingroup$ related: blender.stackexchange.com/questions/12252/face-splitting-tool $\endgroup$ – Dimali Sep 24 '17 at 23:13
  • $\begingroup$ i want to extrude a new plane from point A to point B but sometimes i need to make a curve in between so am asking if theres any way to extrude a vertices from any point of a plane or an edge and make more vertices in the way to other point to control your curve . i hope you get the idea $\endgroup$ – j.alkhalil Sep 24 '17 at 23:15
  • $\begingroup$ This is not extrude but splitting, then there are several tools for that - namely Subdivide (W -> Subdivide), Knife tool (K) and Loop cuts (Ctrl + R). Just fiddle with these on some test scene to see what will work for you. $\endgroup$ – Jan Kadeřábek Sep 25 '17 at 13:40
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You can create a vertex in the middle of the plane poking the plane's face (AltP). Then set the snap type to vertex (CtrlShiftTab -> Vertex) and extrude vertices (select + E) to the plane's middle vertex while holding Ctrl so you have snapping temporarily enabled while dragging. If it is a single object, its even easier - select each 2 vertices and hit F to make a connection (instead of extruding).

I hope this is what you are trying to achieve. enter image description here

UPDATE (after the question was modified):

So you didn't want to extrude anything, you just need to split an edge. Then there are several tools for such task - namely Subdivide (W -> Subdivide), Knife tool K and Loop cuts Ctrl + R).

Just fiddle with these tools on some testing scene to see what will work for you best.

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