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The Cauchy-Length Formula and Holditch Theorem in the Generalized Complex Plane CpErisir, TulayGungor, Mehmet AliGeneralized complex planeCauchy-length formulasHolditch theoremMathematicsIn this paper, firstly, we calculate Cauchy-length formula for the one-parameter planar motion in generalized complex plane C-p which is generalization of the complex, dual and hyperbolic planes. Then, we give the length of the enveloping trajectories of lines C-p. In addition, we prove the Holditch theorem for the non-linear three points with the aid of the length of the enveloping trajectories in C-p. So, the Holditch theorem for the linear three points which is given by Erisir et al. in C-p is generalized for trajectories drawn by the non-linear three points in generalized complex plane C-p.INT ELECTRONIC JOURNAL GEOMETRY2018Articlehttps://rdlopen.rawdatalibrary.net/r/ebyu/169851307-5624enINTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRYinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/16985