The isotomic conjugate of a point is the point of concurrence of the isotomic lines relative
to a point .
The isotomic conjugate of a point with trilinear
coordinates
is

(1)

Vandeghen (1965) calls the transformation taking points to their isotomic conjugates the Cevian transform. The product of isotomic
and isogonal is a collineation
which transforms the sides of a triangle to themselves
(Vandeghen 1965).

An isotomic transversal is sometimes referred
to as an isotomic conjugate (Ehrmann and van Lamoen 2004).

There are four points which are isotomically self-conjugate: the triangle centroid
and each of the exmedian points. The following
table lists some common centers and their isotomic conjugates.

The isotomic conjugate of a line having trilinear equation

(2)

is a conic section circumscribed on the triangle (Casey 1893, Vandeghen 1965).
The isotomic conjugate of the line at infinity
having trilinear equation