Each of the Transform tools (Rotate, Scale, Perspective, etc) can be set to act specifically on paths, using the “Affect:” option in the tool's Tool Options dialog. This gives you a powerful set of methods for altering the shapes of paths without affecting other elements of the image.

By default a Transform tool, when it is set to affect paths, only acts on a single path: the active path for the image, which is shown highlighted in the Paths dialog. You can make a transformation affect more than one path, and possibly other things as well, using the “transform lock” buttons in the Paths dialog. Not only paths, but also layers and channels, can be transform-locked. If you transform one element that is transform-locked, all others will be transformed in the same way. So, for example, if you want to scale a layer and a path by the same amount, click the transform-lock buttons so that “chain” symbols appear next to the layer in the Layers dialog, and the path in the Paths dialog; then use the Scale tool on either the layer or the path, and the other will automatically follow.