The antineutrino scattering channel $bar{ u}_{mu} ,text{CH} rightarrow mu^{+} ,pi^{-} ,X$(nucleon(s)) is analyzed in the incident energy range 1.5 to 10 GeV using the MINERvA detector at Fermilab. Differential cross sections are reported as functions of $mu^{+}$ momentum and production angle, $pi^{-}$ kinetic energy and production angle, and antineutrino energy and squared four-momentum transfer. Distribution shapes are generally reproduced by simulations based on the GENIE, NuWro, and GiBUU event generators, however GENIE (GiBUU) overestimates (underestimates) the cross-section normalizations by 8% (10%). Comparisons of data with the GENIE-based reference simulation probe conventional treatments of cross sections and pion intranuclear rescattering. The distribution of non-track vertex energy is used to decompose the signal sample into reaction categories, and cross sections are determined for the exclusive reactions $mu^{+} pi^{-} n$ and $ mu^+ pi^{-} p$. A similar treatment applied to the published MINERvA sample $bar{ u}_{mu} ,text{CH} rightarrow mu^{+} ,pi^{0} ,X$(nucleon(s)) has determined the $mu^{+} pi^{0} n$ cross section, and the latter is used with $sigma(pi^{-} n)$ and $sigma(pi^{-} p)$ to carry out an isospin decomposition of $bar{ u}_{mu}$-induced CC($pi$). The ratio of magnitudes and relative phase for isospin amplitudes $A_{3}$ and $A_{1}$ thereby obtained are: $R^{bar{ u}} = 0.99 pm 0.19$ and $phi^{bar{ u}} = 93^{circ} pm 7^{circ}$. Our results are in agreement with bubble chamber measurements made four decades ago.
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