Use Delete Points 
to delete points from the currently selected line.
Points may be deleted from all line and area types except Single Stitch. With this object type Insert Points and Delete Points are not available. For columns, a pair of points will be deleted.
Points may also be deleted from emboss lines and MultiWave lines.
Click the Delete Points icon 
, then click the points on the selected object that you want to delete. Stitch angle lines can be removed from satin areas by clicking the hexagonal control point at either end of the line. Right-click to finish.
You may not delete all the points for an object. A fill or satin area must have at least three points. Satin border, motif lines and running, double and triple stitch lines must have at least two points. A satin area must also have at least one angle line. To remove all the points for an object, use Delete 
.
Shortcuts
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Home Tab, Points:
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Keys: Ctrl + D; Alt, H, DP
Delete a Point in a Line
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Click on an object to show the points that make it up.
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Click the Home tab.
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Click the Delete Points icon
, then click the points you wish to delete. They will be removed and the object will change shape accordingly. To remove an angle line for a satin area, click the hexagonal control point at either end of the line.
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Right-click to deselect the function.
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Click and drag to move any of the points in the object to alter its shape.
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If desired, click the Delete Points icon
again and repeat.
The Delete Points icon is only available for objects that can have points deleted.