Isotomic Lines


Given a point P in the interior of a triangle DeltaA_1A_2A_3, draw the cevians through P from each polygon vertex which meet the opposite sides at P_1, P_2, and P_3. Now, mark off point Q_1 along side A_2A_3 such that A_3P_1=A_2Q_1, etc., i.e., so that Q_i and P_i are equidistance from the midpoint of A_jA_k. The lines A_1Q_1, A_2Q_2, and A_3Q_3 then coincide in a point Q known as the isotomic conjugate.

See also

Cevian, Isotomic Conjugate, Isotomic Transform, Isotomic Transversal, Midpoint

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Isotomic Lines." From MathWorld--A Wolfram Web Resource.

Subject classifications