The parity-violating asymmetry arising from inelastic electron-nucleon scattering at backward angle (~95 degrees) near the Delta(1232) resonance has been measured using a hydrogen target. From this asymmetry, we extracted the axial transition form factor G^A_{NDelta}, a function of the axial Adler form factors C^A_i. Though G^A_{NDelta} has been previously studied using charged current reactions, this is the first measurement of the weak neutral current excitation of the Delta using a proton target. For Q^2 = 0.34 (GeV/c)^2 and W = 1.18 GeV, the asymmetry was measured to be -33.4 pm (5.3)_{stat} pm (5.1)_{sys} ppm. The value of G^A_{NDelta} determined from the hydrogen asymmetry was -0.05 pm (0.35)_{stat} pm (0.34)_{sys} pm (0.06)_{theory}. These findings agree within errors with theoretical predictions for both the total asymmetry and the form factor. In addition to the hydrogen measurement, the asymmetry was measured at the same kinematics using a deuterium target. The asymmetry for deuterium was determined to be -43.6 pm (14.6)_{stat} pm (6.2)_{sys} ppm.
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