I have loaded GPS points into a QGIS vector layer. I also imported a vector line from a dxf file which doesn't have georeferencing.
I would like to fit in line geometry between the GPS points - how can I do this?
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Use an affine transformation, basically, you should use one layer as reference (target) and move the other layer (source). Read my answer in this post to get an idea on how to apply it to vector data.