Delete Part of a Polyline Segment - AutoCAD

Question
How do I delete part of a polyline segment WITHOUT using the Trim, Explode or Pedit commands?

Answer
For this to work you need AutoCAD 2011 or newer, as it contains some new fancy sub-selection routines for both 2D and 3D.

Also check that the LEGACYCTRLPICK variable is set to either ‘0’ (zero) or 2 (The default setting is 2) this will not work if this variable is set to ‘1’

Draw your polyline, rectangle or polygon or whatever.

When modifying hold down the CTRL Key (just the segment will highlight) select it and Press the Delete key on the keyboard.