When importing a JPG map using QGIS's georeferencer plugin, the resulting map layer is distorted and does not look anything like the map that I am trying to import. I can't work out what is causing this map distortion.
Screenshots of the steps
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If you're using just two points for georeferencing try using "Helmert". Definitely not thin plate spline. The map looks to be for somewhere in England, so set the target CRS to EPSG:27700.
The distortion is caused by your selection of target SRS, and the CRS you are using in your QGIS project.
As soon as you are using a different CRS in QGIS as the one used to create your the raster (jpg file), you will see this distortion.
This normal behaviour.
If you're setting the same CRS to the QGIS project, the image shown will resemble your original data (providing you have performed a correct georeferencing).