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I have a line with a point in the center (2 edges with 3 points that forms a straight line). How do I slide the middle point along the straight line it resides on?

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Using Vertex Slide:

Select the point and press ShiftV or GG. Then move it to the desired point on the line with the mouse and click to set it. Hold Alt to slide it past the end of the edge.

Alternatively, this can be reached through the Edit Mode toolbar menus: Vertex -> Slide Vertices:

Vertex -> Slide Vertices

Or through the right-click context menu:

Context menu -> Slide Vertices

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    $\begingroup$ You can also enable Vertex Slide by pressing G twice $\endgroup$ – Haunt_House Sep 18 '13 at 5:12
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    $\begingroup$ @Haunt_House great tip! That seems to work with edges too for edge slide. $\endgroup$ – z0r Sep 18 '13 at 12:22
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    $\begingroup$ It's also accessible with Ctrl+V > Vertex slide $\endgroup$ – gandalf3 Sep 18 '13 at 16:14
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Just for the record, if you are using a very old version of blender that does not have vertex slide functionality:

  1. Select one of the end vertices
  2. Shift S --> Cursor To Selected
  3. Select the middle vertex
  4. . (period) Set cursor as pivot point
  5. S Now you can move the middle vertex along the line
  6. When you are done, reset the pivot point with , (comma)
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Select the vertex and use Shift V or GG to move along the edge.

http://blenderbits.com/2013/09/02/blender-vertex-constraints-on-faces/

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