Answer
The Define Projection tool is used to apply a projection to data that does not have a projection defined, or has the projection defined incorrectly. The projection definition selected must match the coordinates the data are projected to.
For example, the coordinate pairs below all describe a specific USGS Survey Control Point, in different coordinate systems. When defining a projection for this point, the projection definition must match the coordinate system that point is in:
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U.S. Geological Survey Level 1 Survey Control Point
DESIGNATION - FAA L12 A
PID - EV9276
STATE/COUNTY- CA/SAN BERNARDINO
USGS QUAD - REDLANDS (1996)
Coordinate System X-Coordinate (Longitude) Y-Coordinate (Latitude)
GCS_NAD_1983_HARN decimal degrees -117.147115997222222 34.084757672222222
NAD 1983 State Plane CA_V, FIPS 0405 Feet 6,819,912.12 1,854,322.74
NAD 1983 UTM Zone 11 Meters 486,427.659 3,771,563.570
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If data is received in a coordinate system that does not match your other data, use the Project tool in ArcToolbox. The Project tool creates a new copy of the data, in the coordinate system selected.
For example, if data is received in a Geographic Coordinate System (GCS), use the Project tool to create a new set of data in State Plane, UTM, or some other coordinate system to match your other data.
Note:
The projection must be defined correctly before you can project the data to a new coordinate system.
For further information on this topic, see the Related Information section below to access Knowledge Base article 23025, Projection Basics: What the GIS professional needs to know, Knowledge Base article 29129, Identify the spatial reference, projection or coordinate system of data, and other related articles that have instructions for identifying the coordinate system for data that does not have a projection already defined, and where metadata is not available.