I have a map project wih layers in WGS1984 UTM projection. I also have a bunch of layers without .prj files. When I add it on top of my layers, it's placed with a huge offset on X and Y coordinates but other than that everything is fine, features are not distorted etc. So basically I just need to "move" all the features along X and Y axes and everything will be alright.
Can I define such projection using ArcGIS "Define projection" tool or something else? I need a projection that just adds a linear offset to X and Y coordinates. I know I can fix one layer by using "Spatial Adjustment" tool and it works fine, but my goal is to have a .prj-file that I can use for any such layer.
I'm kinda new to ArcGIS and will give clarifications if needed. Any help would be appreciated, thanks in advance.