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For ArcMap 10.3: I had two shapefiles, that at one point, were in different coordinate systems. Shp#1 was in NAD_1983_Texas_Centric_Mapping_System_Albers and Shp#2 was in NAD_1927_StatePlane_Texas_Central_FIPS_4203 and those were good times, as the shapefiles were then only 30 or so feet apart. But, I wanted complete accuracy in editing Shp#1 to Shp#2's minor detail change, so I attempted to change the coordinate system on Shp#2 in ArcCatalong by right clicking and going to properties and bring it over to NAD_1983_Texas_Centric_Mapping_System_Albers at which point it got even further away across my map in two completely different locations. I have performed a Define tool in ArcToolbox and a Project tool in ArcToolbox but to no avail-- it stays put in the exact same spot. I have checked MetaData-- no answers. The mouse hovers over the coordinates of each in meters as it should. I will probably geo-reference it as my last resort, but just out of curiosity I'd thought I'd try here to see if someone could explain to me why exactly something like this would happen.