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I have a geographic file (be it shapefile or otherwise) which is stretched and dislocated into the wrong projection space.

So I'm wondering how to approximate its correct location by selecting points on this file which correspond to real-life locations in the given basemap, and use this knowledge to correctly geo-reference it in the way we would with most raster images?

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    Before going this way, I'd try to figure out the real projection of the file and assign this crs to it.
    – MrXsquared
    Commented Jan 26, 2021 at 0:41
  • I have, but it didn't work with any fruitless or futile search, and seems only to be an approximation anyway. Besides, I suspect this may be quicker and in any case, the co-ordinates are off (shunted to the side of) so I will need to re-align the projection anyhow
    – Anna
    Commented Jan 26, 2021 at 0:45
  • See: gis.stackexchange.com/questions/33208/… There are a few correct answers there.
    – HeikkiVesanto ♦
    Commented Jan 26, 2021 at 1:15
  • @HeikkiVesanto thank you, do any of these replicate the ease and simplicity with which we can now import an image onto QGIS project file for viewing and distortion purposes in terms of usage and basemap layer?
    – Anna
    Commented Jan 26, 2021 at 2:00
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    Try to use Georeference a shpefile with use of qgsAffine Plugin or Vector Affine Transformation Plugin by Mauricio de Paulo and Erik Timmers. plugins.qgis.org/plugins/qgsAffine
    – Uditha Herath
    Commented Jan 26, 2021 at 8:27

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Since QGIS 3.26 this can now be achieved with the georeferencer, same tool that is used of raster georeferencing:

"QGIS now supports georeferencing vector layers in the georeferencer tool. This allows vector layers without spatial referencing to be interactively georeferenced, or layers with referencing to be re-referenced, in a similar manner to raster data. Georeferencing occurs in a task, so QGIS should remain responsive, even with large datasets."

https://www.qgis.org/en/site/forusers/visualchangelog326/index.html#feature-georeferencing-vector-layers-in-georeferencer

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