Homothetic transformations and geometric loci: properties of triangles and quadrilaterals

Maria Flavia Mammana ^[1]
1. [1] University of Catania
  
  University of Catania
  
  Catania, Italia
Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 47, Nº. 7, 2016, págs. 1103-1119
Idioma: inglés
DOI: 10.1080/0020739x.2016.1164345
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Resumen
- In this paper, we use geometric transformations to find some interesting properties related with geometric loci. In particular, given a triangle or a cyclic quadrilateral, the locus generated by the centroid or by the orthocentre (for triangles) or by the anticentre (for cyclic quadrilaterals) when one vertex moves on the circumcircle of the figure are considered. These loci are studied in paragraphs 3 and 4. By means of the homothetic transformations some properties of triangles and quadrilaterals are found. The study of these properties can be used, with profit, in a classroom activity supported by Dynamic Geometry System.