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] λ5007 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 ~12,000 to 15,000 K), while the densities vary from a few tens to a few hundred per cubic centimeter. The emission mechanism of all of the emission clouds, as indicated by the line-ratio diagnostics, is consistent with both ``shock + precursor'' and pure photoionization models. The total mass of the ionized gas is on the order of 109 Msolar. We estimate a bulk kinetic energy and momentum of the extended emission-line region of 2.5×1057 ergs and 1050 dyn 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 of the feedback of the quasar. We also discuss the nature of the extended X-ray emission surrounding the quasar. Based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Particle Physics and Astronomy Research Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), CNPq (Brazil), and CONICET (Argentina).
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