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Find Coordinates of a point on a line with minimal information

I am creating a program that can draw sewing patterns based on a person's measurements. The reference material I have assumes you are working on paper, thus some of the problems I am having. I am writing a function that creates points that I can then use to draw the pattern. In some cases the points are simply reference to draw other points and won't actually be displayed. Also, just to make things more complicated, I am switching from inches (reference material) to centimeters.

I attached the reference page I'm working with to better understand what I'm talking about. I also put in all the points that I've calculated so far.

I wasn't having any problems until I started working with the angled lines. My first roadblock was Figure 2 line B-G. We used the pythagorean theorem with line A-C length (17.78), line B-G length (43.498) to come up with the line length to get the y coordinate for G. If that was a mistake, please let me know.

Assuming that the G coordinate is correct, now I have to find the H coordinate. I have absolutely no idea how to do this. The only measurement I have is that it's 22.86cm from G to H. Since I have the full triangle from calculating G, I can now get the slope of B-G, if that helps.

I don't even know if this is a geometry or trig question, so I apologize if I'm asking in the wrong place. Any advice would be greatly appreciated.

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Re: Find Coordinates of a point on a line with minimal information