What Yagi driven element feed point impedance is required to use a beta or hairpin matching system?
Why A beta or hairpin match is simply a shorted transmission line stub or wire loop placed in shunt across the feed point, and it acts as an inductor. For that shunt inductance to form a working L-network, the driven element itself must supply the opposite (capacitive) reactance, which means it is tuned slightly short of resonance, electrically shorter than 1/2 wavelength. The shunt inductor cancels that capacitive reactance and at the same time transforms the element's low radiation resistance (often 20 to 25 ohms on a close-spaced Yagi) up to the 50 ohms the feed line wants.
Watch out An inductive (electrically long) element is what a gamma or omega match wants to work against, since those add series capacitance; adding a shunt hairpin inductor to an already inductive element only makes the mismatch worse. A purely resistive element needs no matching network at all.
Hairpin = inductor, so the element must be capacitive: short element, shunt coil, reactances cancel.