If you are allowed to assign "arbitrary" weights to a point / line, then yes a particular line can have an area of 1.

E.g. If we assign the origin a dirac delta weight of 1, and no weights to any other point, then any line through the origin has an "area" of 1. In fact, a figure has an area of 1 if and only if it contains the origin.

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TopNewestIf you are allowed to assign "arbitrary" weights to a point / line, then yes a particular line can have an area of 1.

E.g. If we assign the origin a dirac delta weight of 1, and no weights to any other point, then any line through the origin has an "area" of 1. In fact, a figure has an area of 1 if and only if it contains the origin.

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