Construct a Harmonic Set of Points

Check the box for each step of the construction in order to illustrate the steps of the constructive proof of Theorem 4.6. If A, B, and C are three distinct collinear points, then a harmonic conjugate of C with respect to A and B exists.

Is the fourth point unique or does it depend on the quadrangle constructed?
To investigate this question, drag points E and F to various locations
To change the harmonic set, drag points A, B, and C.

What happens when E and F are moved?
Does the quadrangle remain the same?
Does the fourth point, D, of the harmonic set remain in the same position?

Timothy Peil, 5 February 2013, Created with GeoGebra