Isotomic Regions

The isotomic conjugate: Each sense of center leads to a sense of deviation from center. For points the obvious center is the midpoint; for lines it is the angle bisector. For points the deviation from center is the distance from the midpoint. Equal deviations are called isotomic.

Consider a point P in the plane of the triangle. The intersection of the Cevian lines through P with the triangle edges are called the Cevian traces of P. The isotomic conjugate of P is formed by the concurrence of the lines formed from the reflections of the traces over the midpoint of its edge.

Figure: Along each edge, the traces of P and its isotomic conjugate tP are equally spaced to the midpoint.

This page shows how a point relates to its isotomic conjugate. This page is taken from The Triangle Book and are the shape and size that the book will probably be. Some details came from my own research. Another page shows isogonal regions.