Line-inversion and pedal transformation in the quasi-hyperbolic plane

The line-inversion and pedal transformation are defined in the quasi-hyperbolic plane and certain properties of these transformations are shown with regard to analogous transformations in the Euclidean [1, 3, 10, 12, 20], hyperbolic [4, 15, 18] isotropic [17, 19] and pseudo-Euclidean plane [5, 6, 7, 14]. As it is natural to observe class curves in the quasi-hyperbolic plane, i.e. line envelopes, the construction of a tangent point on any line of the class curve obtained by the line-inversion and pedal transformation is shown.