Projective Harmonic Conjugate - of Midpoint

Of Midpoint

When x is the midpoint of the segment from a to b, then

By the cross-ratio criterion, the projective harmonic conjugate of x will be y when t(y) = 1. But there is no finite solution for y on the line through a and b. Nevertheless,

thus motivating inclusion of a point at infinity in the projective line. This point at infinity serves as the projective harmonic conjugate of the midpoint x.