= Solution
{c}
$P_1$ has primitive coordinates $(1/2,1/2)$ and therefore fails the first-order optical momentum condition; its local $V_1$ pattern also has zero dipole derivative. $P_2$ is a zone-centre mode with the dipole-active $V_2$ pattern, so its molecular dipole changes add coherently.
$$
\boxed{P_1\text{ is IR inactive};\qquad P_2\text{ is IR active}.}
$$
The allowed absorption for $P_2$ uses an <polarization of an electromagnetic wave> with an out-of-plane component. At normal incidence on an ideal free-standing layer the electric field is in the plane, so that specific measurement geometry would suppress it despite the mode's intrinsic <vibrational infrared activity>.
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