Following the earlier discovery of classical Cepheid variables in the Sculptor Group spiral galaxy NGC 7793 from an optical wide-field imaging survey, we have performed deep near-infrared $J$- and $K$-band follow-up photometry of a subsample of these Cepheids to derive the distance to this galaxy with a higher accuracy than what was possible from optical photometry alone, by minimizing the effects of reddening and metallicity on the distance result. Combining our new near-infrared period-luminosity relations with the previous optical photometry we obtain a true distance modulus to NGC 7793 of $(27.66 pm 0.04)$ mag (statistical) $pm 0.07$ mag (systematic), i.e. a distance of $(3.40 pm 0.17)$ Mpc. We also determine the mean reddening affecting the Cepheids to be $E(B-V)=(0.08 pm 0.02)$ mag, demonstrating that there is significant dust extinction intrinsic to the galaxy in addition to the small foreground extinction. A comparison of the new, improved Cepheid distance to earlier distance determinations of NGC 7793 from the Tully-Fisher and TRGB methods yields agreement within the reported uncertainties of these previous measurements.
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