We present Gemini Multiobject Spectrograph integral field spectroscopy of the extended emission-line region associated with quasar 3C 249.1. The kinematics of the ionized gas measured from the [O III] $lambda$5007 line is rather complex and cannot be explained globally by a simple dynamical model, but some clouds can be modeled individually as having locally linear velocity gradients. The temperatures of the ionized gas appear uniform (varying from ~12000 to 15000 K), while the densities vary from a few tens to a few hundreds cm^{-3}. The emission mechanism of all of the emission clouds, as indicated by the line-ratio diagnostics, is consistent both with shock + precursor and pure photoionization models. The total mass of the ionized gas is on the order of 10^9 M_Sun. We estimate the bulk kinetic energy and momentum of the extended emission-line region of 2.5*10^{57} ergs and 10^{50} dyne s, and a dynamical timescale of ~10 Myr. By comparing the injection rates of kinetic energy and momentum of different galactic wind models with the observation, we argue that the emission-line clouds are most likely a direct result from the feedback of the quasar. We also discuss the nature of the extended X-ray emission surrounding the quasar.
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