2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61966In the first part of this investigation, [Ha], we generalized a weighted distance function of [Li] and found necessary and sufficient conditions for it being a metric. In this paper some properties of this so-called M-relative metric are established. Specifically, isometries, quasiconvexity and local convexity results are derived. We also illustrate connections between our approach and generalizations of the hyperbolic metric.23 pages, 2 figuresMetric GeometryClassical Analysis and ODEsPrimary 39B62, Secondary 26D07, 30F45text