mcrowder-- alternative (b) of the OP refers to a tag attempt: "b) as soon as he backs up three feet to avoid the tag;"
GarthB-- You have quoted the old rule, not the new rule. I did helpfully point out that the rule has changed, and that fact may alter interpretation, but you don't seem to have read for comprehension.
And of course a line is between two points. I think the new rule specifies the two points they have in mind, and in this situation (as opposed to a runner between his occupied and advance base, in which case there are generally two baselines defined by 3 points) one of the two points is the runner himself.
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