B

Given a rod sliding down a wedge with angle \( \theta \), we can analyze the motion using geometry.
Step 1: When the rod moves down by a distance of \( x_1 \), it will cause the wedge to move horizontally.
Step 2: The relationship between the vertical displacement \( x_1 \) and the horizontal displacement \( x_2 \) of the wedge can be derived from the geometry of the situation:
\( x_2 = x_1 \cdot \tan(\theta) \)
Therefore, if the rod slides down by \( x_1 \), the wedge will move by \( x_2 = x_1 \cdot \tan(\theta) \). Hence, based on the options given, the correct answer is option B.