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Is there a way to slide a vertex along a line until an intersection of another line, which has no vertex at said intersection like it is shown in the picture?

I am a total beginner in blender and couldn't figure this out by searching for tutorials,

vertex slide until intersection

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3 options to create a vertex at the intersection between two edges:

  1. Activate and use The tinyCAD shipped add on > V2X: 'Vertex at Intersection'

  2. EExtrude the edges to make faces, select them, and search for 'Intersect' (Spacebar in 2.79, F3 in 2.80). Check the 'Self Intersect' option. Delete excess vertices.

enter image description here

  1. Create a plane below the edges, and Knife Project the edges down onto the plane, which will create a vertex at the intersection between the projected edges, (and possibly some surplus geometry) That vertex can become a snap target, or you can duplicate the edges out of the plane.

enter image description here

This last method can sometimes be quite useful .. the lines only have to intersect in your chosen projection, which you define by the orientation of your plane, before Shift Numpad 7 aligning your view to it, to execute the Knife Project.

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Slide using Shift+V

Make sure snapping is on.. and set to vertex - closest .. and you will snap to the vertex on intersection.

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    $\begingroup$ You can't snap to geometry while vertex or edge sliding $\endgroup$ – Duarte Farrajota Ramos Jun 20 at 2:58

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