Let A, B, and C be complex numbers which represent the vertices of a triangle in the complex plane. Using these complex numbers and their complex conjugates write an expression which represents the point B reflected about the line AC. Use X' to denote the complex conjugate of the complex number X.

I get A+(B-A)'(C-A)/(C-A)'.  I used a linear (affine linear, to be more accurate) map to map A to 0 and C to 1, and then I mapped back the conjugate of the image of B. The mapping preserves angles and uniformly scales distances on any given line. One notes that (C-A)/(C-A)' has unit magnitude and angle twice what the line AC makes with the horizontal.

Edited on April 20, 2006, 1:08 am

Posted by Richard on 2006-04-19 20:30:49