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So make the load on the end of that feed line (the antenna) the same impedance as the feed line (and the rest of the antenna system) and that SWR won't change no matter it's length.

That's the simple answer.  If you want to know 'why', then it get's complicated because impedance is composed of resistance and reactance.  There are various compositions of resistance and reactance that will 'equal' the desired impedance and still not be the 'ideal' 50 ohms and zero reactance desired.  One 'catch' is that an SWR meter can't tell the difference between resistance and reactance, it can only indicate/display the combination of the two.

RF is alternating current.  ALL alternating current has impedance and therefore resistance and reactance.

If it ain't one thing, it's another, right?

 - 'Doc