What comparison can be made regarding the physical distance and apparent brightness of Alnitak relative to Mintaka?

Answer

Alnitak is farther from Earth than Mintaka, yet its intrinsic luminosity must be much greater to appear nearly as bright.

Despite Alnitak being physically farther away from Earth than Mintaka, its apparent magnitude (+1.8 vs +2.2) shows it must possess a significantly greater intrinsic luminosity.

What comparison can be made regarding the physical distance and apparent brightness of Alnitak relative to Mintaka?
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