Generalizing robot trajectories from human demonstrations to new contexts remains a key challenge in Learning from Demonstration (LfD), particularly when only single-context demonstrations are available. We present a novel Gaussian Mixture Model (GMM)-based approach that enables systematic generalization from single-context demonstrations to a wide range of unseen start and goal configurations. Our method performs component-level reparameterization of the GMM, adapting both mean vectors and covariance matrices, followed by Gaussian Mixture Regression (GMR) to generate smooth trajectories. We evaluate the approach on a dual-arm pick-and-place task with varying box placements, comparing against several baselines. Results show that our method significantly outperforms baselines in trajectory success and fidelity, maintaining accuracy even under combined translational and rotational variations of task configurations. These results demonstrate that our method generalizes effectively while ensuring boundary convergence and preserving the intrinsic structure of demonstrated motions.