This posting with specific regard to the prior – Rhombi, Trapezia, and a Case of Pythagorean (et al.) Expansion – of July 4, 2022.
Alternative to the employment of lateral trapezia height to ascertain a triangle’s proportional center for use as a center of dilation, the following may be applied:
Where b lies along the x-axis and a intersects at x0y0 and within the isosceles limitation that occurs where c=b
Interesting is a trace of the proportional center’s path for a given a:b ratio. As example, an a:b of .75 would likely appear as follows (note the extending of the path beyond the isosceles inversion):
