I am trying to rotate a polygon layer around a point but the affine tool keeps moving the polygon far away from where it needs to be. I'm using the affine calculations found in this stack exchange question to move the polygon. Doing a translation-only move works fine and as expected. But when I try to rotate a polygon, it shifts the whole polygon far away. Then when I try to undo that, it won't put the polygon back where it was originally. I think it's an issue with my projections, but even with 'on the fly' projections turned on it still won't draw it correctly.
A little background: I got an ArcGIS data set that had no other projection info included, just the shp and dbf files. After importing the data into a new QGIS project with a WGS 84 projection for my project, I had to guess at the layer projection until one worked that got the existing polygons close to where they should be, but it wasn't perfect. So I have been moving the layers using the affine tool and, again, the translation works fine, but rotation gives strange results moving the polygons far away. Even exporting the layer to the the same projection as the project and trying the affine rotation on that does not work. It seems to be a projection issue, but I can't figure out what the correct settings should be.