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Displaying offset of coordinate pair collected in different GCSs

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I am stumped. I want to demonstrate how coordinates "assigned" to different datums will be offset.

I start with a lat/long coordinate pair. In ArcGIS I 'Display XY coordinates' and assign first the GCS NAD 27. I do the "Data > Export Data" process to create a shapefile from the Event layer and make sure to preserve the NAD27 CS. I have gone so far as to restart my computer, restart ArcMap, then display the XY coordinate pair again, this time assigning it to the GCS NAD 83 and follow the same steps to create a point file. The coordinate point is in New Mexico and should be offset by approx. 60+ meters. But every time I try this, the points display exactly coincident in space.

Is ArcMap able to see that the coordinate values are the same and tries somehow to "correct" this by displaying them in the same location even though I've told Arc that one was collected in NAD 27 and the other in NAD 83?

I've used several computers, several versions of ArcGIS (9.3, 10.1, 10.2) and have even tried adding 0.00000000001 to the decimals of the NAD 83 coordinates just to see if that would "trick" ArcGIS into not recognizing them as the same coordinate values.

This isn't a problem of 'projecting on the fly' because the coordinate pair are being assigned to different coordinate systems. They should in every instance display in different locations.

As a side note, when displayed in Imagine the points display 53 meters apart.
Any ideas?

Shannon

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