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Planets and moons reorient in space due to mass redistribution associated with various types of internal and external processes. While the equilibrium orientation of a tidally locked body is well understood, much less explored are the dynamics of the reorientation process (or true polar wander, TPW, used here for the motion of either the rotation or the tidal pole). This is despite their importance for predicting the patterns of TPW-induced surface fractures, and for assessing whether enough time has passed for the equilibrium orientation to be reached. The only existing, and relatively complex numerical method for an accurate evaluation of the reorientation dynamics of a tidally locked body was described in a series of papers by Hu et al. (2017a,b, 2019). Here we demonstrate that an identical solution can be obtained with a simple approach, denoted as ow||mMIA, because, contrary to previous claims, during TPW the tidal and the rotation axes closely follow respectively the minor and the major axes of the total, time-evolving inertia tensor. Motivated by the presumed reorientation of Pluto, the use of the ow||mMIA method is illustrated on several test examples. In particular, we analyze whether reorientation paths are curved or straight when the load sign and the mass of the host body are varied. When tidal forcing is relatively small, the paths of negative anomalies (e.g.~basins) towards the rotation pole are highly curved, while positive loads may reach the sub- or anti-host point in a straightforward manner. Our results suggest that the Sputnik Planitia basin cannot be a negative anomaly at present day, and that the remnant figure of Pluto must have formed prior to the reorientation. Finally, the presented method is complemented with an energy balance that can be used to test the numerical solution.