""""", I'd like to suggest that clicking on a corner grip of a selected line would indicate the position that remains fixed when it is resized. In fact, might that also be useful when resizing any object via the Edit size window?"""""

Hey Martin,
That is in the edit frame already. When you click on a corner widget, you'll see the center ball move to the other side, indicating the origin location (The rotation widget can be placed "anywhere", when in rotation mode)

Although, it doesn't do this when using the properties size edit, like you point out....