I have three shapefiles exported from a CAD drawing (point, polygon, polyline). Judging by where the CAD drawing came in when I first added it as data, it is in a different coordinate system (the architect who sent it seems to like WGS 84; however, I'm using NAD 83 State Plane Texas Central FIPS 4203 since that is what the county uses). Changing the coordinate system in ArcCatalog doesn't 'move' these to where it should be.
What am I doing wrong? Sometimes ArcMap will flag me to do a transformation when I add data with a different coordinate system, which usually fixes things. Is there any way to do an 'on demand' transformation on these CAD-derived shapefiles?