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How can I generate a table with measured distances between two related point layers?

Every point from A layer has at least 1 assigned point in B layer and the attribute that defines relation between them is saved in separate table (A layer->table-> B layer). I have made relations in arcGIS to define pairs of points. Now I need to know what is the distance between them.

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You can try to use Generate Near Table tool if you have ArcGIS for Desktop Advanced license. Another way is writing a script using arcpy library. See distanceTo method (the distance between the two geometries).

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I would recommend Points To Line and then calculate the geometry (length) of the resulting lines.

You say you have a relationship established already so this tool can use that key field to connect the dots between related points and ignore other non-related points that might be close by.

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