Buck wrote:

ok, a 100 ohm load fed with 50 ohm coax is a 2:1 swr. Fed with 75 ohm
coax, it is 1.33:1 ??

If the 75 ohm is fed with 50 ohm coax 1/4 wave down the 75 ohm coax,
it will be a close match?

Why did the impedance change to 52 ohms?

Because of the energy bouncing back and forth between the 100 ohm load
(that mismatches the 75 ohm, so causes a reflection) and the 50 ohm
feed (that mismatches the 75 ohm section, so causes a reflection).

If the 1/4 wave section has an impedance that is the geometric mean of
the impedance on each end, it creates a perfect matching resonator.

So the perfect 1/4 wave matching section between 50 and 100 ohms would
have an impedance of the square root of (50 times 100) or 70.7 ohms.
75 is pretty close.