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A line is (theoretically) one-dimensional, so I would say to scale from center of the line.
You can calibrate your printer, but even that doesn't fix the problem because a copy of the drawing will still have its own distortion. This is why drawings usually say "Do not scale drawing".
We also have scale issues with our printer. It is an HP Designjet. However, in the Windows system printer settings, I can't find anything to calibrate it. It is an issue when we do long plots (like 6'). It is consistent in its error, and I was able to us AutoCAD to create a plotter calibration.
Is there a generic way to calibrate a plotter in SW, like in AutoCAD? Am I missing something with my HP Designjet.... I am surprised there wasn't a calibration option in the printer setup.
For years we printed burn templates at 1:1 on both Solidworks and Autocad. Some were in excess of 25 feet long. There was some slight variance in length due to plotter accuracy, rolled paper and even temperature, but overall ran pretty close, usually within 1/8" - 3/16" over that length. It was always in length. Width was always spot on.
We used a Designjet and somehow our IT guy was able to calibrate it, because every so often it would start printing bad and had to be recalibrated. It was somewhere in the setup options. Unfortunately I don't work there any more.
I think the biggest danger you have is that you don't know how accurate the mylar was plotted - it could be off, too.
I've never been a fan of scaling drawings when there are other ways around that - I prefer to scan them. You can then either use a raster to vector conversion program, or you can insert the image into Autocad and trace it manually.
Scanning, however, can introduce more trouble for you if the scanned item gets "stretched" going through the scanner.
If you don't have a scanner, check the yellow pages. Here in Houston there are several companies that will scan even large drawings for a few bucks. But if yours are REALLY large, that may not even be an option for you.
As far as dimensioning, I usually go for the center of the line. This is easier with a scanned image inserted in Autocad because you can zoom in pretty close and see the individual pixels and you can mostly tell where the real "center" of the line is.
Not sure if the OP has a Designjet, but there is a calibration for them - it's in the menu somewhere (I'm talking about the 800 series, which I hate...) Regardless, you should be able to find a PDF of the manual at the MFG website for the plotter.
Good luck with your project - I know it isn't fun!!