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I'm performing measurements of distances in Km between a lot of localities by using the "Point Distance" in ArcGis 9.3. I realized that the results obtained after using projected coordinate system are the same of those obtained without projecting data. I change projected coordinate system in "Data frame properties". Where am I wrong? I am a newbe in Gis and in ArcGis too. Any advices will be invaluable. Thanks in advance.

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There is a difference between 1) the coordinate system of the dataset, and 2) the coordinate system of the data frame that your dataset may be projected into through ArcMap. The geoprocessing tools will use the projection of the dataset and not the reprojected coordinates of the data frame in ArcMap because the geoprocessing tools (such as Point Distance) operate independantly of whatever display wackiness is happening in ArcMap.

Also, do you know the projection that your data was captured in? If that projection (regardless of it whether or not it already has a projection assigned to it or not through ArcGIS) is the same as the projection you're trying to set to in the data frame, then the measured units will be the same. Eg. if your data is already in NAD83 UTM Zone 15, but just doesn't have coordinate system assigned to it, deliberately assigning that same projection to the dataset won't affect the coordinates or relative distances at all.

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e-falcon, based on your comments below, you're not actually reprojecting the shapefile - you need to find the 'Project' tool which is buried somewhere under the 'Data Management' tools. You will, however, need to accurately define your source projection (what your data is currently in). –  WolfOdrade Jan 14 '11 at 17:07
    
the comment Wolf refers to is "in ArcCatalog I simply went to shapefile properties->XY Coordinate System. Then I pressed “Clear” to delete any previous information. The second step was to select “New” to choose a new Projected Coordinate System (Mollweide, with Central Meridian set to a specified value). The third step was to select the Geographic Coordinate System and I chose ->World->WGS 1984.prj. Then I loaded the shapefile in ArcMap and performed “Point Distance”. Where is the mistake?". It was submitted as an answer and not a comment, since deleted to clean up the question. –  matt wilkie Jan 17 '11 at 17:34

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