Let 
and 
be points in trilinear coordinates, neither
of which is on a side line of a reference triangle 
. Them the 
-isoconjugate of 
is the point
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Isogonal and isotomic conjugations are examples of isoconjugations.
The earliest appearance of the term "isoconjugate" in triangle geometry may have been by Kimberling as early as 1998. Isoconjugates were also discussed in Kimberling (2001, 2002). Thereafter, the term "isoconjugate" has sometimes been used to mean reciprocal conjugate, which is a different sort of conjugate (Kimberling).
