Explanation: A quarter-wavelength matching line, also known as a quarter-wave transformer, is a specialized transmission line section used to match two different impedances. Its surge impedance (characteristic impedance, $Z_0$) is critical for this transformation. The correct formula dictates that the characteristic impedance of the quarter-wavelength matching line must be the geometric mean of the two impedances it connects. If $Z_{ant}$ is the antenna impedance and $Z_{line}$ is the impedance of the main feedline (or the other impedance being matched), then the surge impedance of the matching section, $Z_0$, is given by: $Z_0 = \sqrt{Z_{ant} \times Z_{line}}$ This relationship ensures maximum power transfer between the source and the load by transforming one impedance to match the other. Option C, when correctly interpreted as $Z_0 = \sqrt{\text{impedance of antenna} \times \text{impedance of line}}$, aligns with this fundamental principle of quarter-wave impedance transformers. Options A and B present formulas that do not correspond to the established theory for determining the surge impedance of a quarter-wavelength matching line.