When in doubt, here's a clue. Works top and bottom (though on the upper side of males it is often faint). Mariposa differs from it's closest relatives (as well as most similar), the Lilac-bordered, Purplish, and Dorcas Coppers, in the placement of the dark spot closest to the lower outer corner of the front wing (or sometimes it's broken into a pair of dark spots). In Mariposa it is pretty much in line with the two spots above it. In the other three the same spot is obviously offset toward the base of the wing and away from the outer margin as compared to the spots above it (at least nearly always; in occasional individuals it is hard to call). Usually checkered fringes help with Mariposa, but in worn or damaged specimens the fringe may be gone. In both of these you can see the checkered fringe most clearly on the front left wing (perhaps due to lighting), and the placement of the dark spot on the front wing is cearly visible. The underside can even be difficult to distinguish in really worn specimens, but that spot almost always works (maybe better than 99% of the time), and it never moves as the butterfly ages.

Now as for telling the other three apart - well, for two of them anyway, that's a very difficult, debated, and rather long topic for another place.

Moved from Butterflies and Skippers.

Moved from ID Request.

Lilac-bordered Copper, the range of which barely extends to Manning