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For what it's worth (and it's not worth much on a softball rules forum), I can confirm that in FED baseball the "imaginary line" running from first to third base is used for determining a fair or foul call. This is spelled out in their "Base Hit/Fair Ball" definition under rule 2.
I've never found such an interpretation for softball, but can imagine some confusion arising in associations that handle umpire training, registration and certification for both baseball and softball.
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