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I have a path which I rotated 45 degrees. I want to make it longer without changing the width. Is there any way to do it other than scaling the original path and then rotating it 45 degrees?

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If it's still a rectangle element, and you haven't converted it to paths, then you can use the Rectangle tool to select it. Then you can change the width or height numerically in the controls bar along the top. You could also click on the rectangle controls to resize it manually.

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If you converted the object to paths, there's no simple method. One possible workaround is if there is a transform applied. It would then be possible to open up the XML editor, and delete the transform. Then select the end nodes with the Nodes tool, and move them while holding down Ctrl. Then do the rotation again.

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Another possible workaround is to duplicate the object, do Object > Object to Guides, select the end nodes with the Nodes tool, and with snapping on you can reposition them so they snap to the guides.

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