Hi Eric,
Again you've done exactly what I wanted. Regarding the horizontal line I mentioned, I inserted a line in your Manipulate that visually gives what I am seeking. The imitation of my code for the line is that the Locator is not really constrained to the horizontal line.
Manipulate[Graphics[{GrayLevel[.5],
Line[{{-5, 0}, {5, 0}}],
Line[{-.5 length {Cos@angle, Sin@angle}, .5 length {Cos@angle,
Sin@angle}}], Black, Point[{0, 0}], Blue,
TranslationTransform[p][
Line[{-.5 length {Cos@angle, Sin@angle}, .5 length {Cos@angle,
Sin@angle}}]]},
PlotRange -> 10], {{p, {0, 0}}, {-5, 0}, {5, 0},
Locator}, {{angle, Pi/4}, 0, Pi}, {{length, 3}, 1, 5}]
I expect that I will eventually figure out how to make the Locater slide under constraint. However, if you are able to pass along that result, I would be most grateful.
I must admit that I barely understand the program you have written for me, but it is perfect to study because it does not include anything of unimportance that could be distracting. You have helped me avoid perhaps many weeks of perplexity. I compliment you on your programming skill and your willingness to share it. Thank you too, but saying so seems hardly adequate.
William Stockich
By the way, my goal is to illustrate a research paper. It is from Descartes' Geometry, 1637, and this geometric construction is an example of the very first treatment of a 2nd degree equation in analytic geometry in revolutionary notation which is used to this day.
While Descartes' math appears to be modern, his way of explaining it is so convoluted that in the nearly 400 hundred years since, very little has published attempting to explain what he was doing. It's not complicated but I'm guessing that any explanatory study has been too time-consuming to be worth the effort.