Isogonal and isotomic conjugates of a triangle

The positions and properties of a point in relation to its isogonal and isotomic conjugates are discussed with use of the dynamic program The Geometer’ s Sketchpad. Special attention is attached to the well-known triangle points as the four remarkable points of the triangle (incenter, circumcenter, orthocenter, centroid) and some other points as Gergonne point, Nagel point, Lemoine point etc. Finally formal properties of the isogonal and isotomic transformation are shown.