Final answer:
The distance from the equilibrium position to the crest is equal to the distance from the equilibrium position to the trough, and both represent the amplitude of the wave.
Step-by-step explanation:
The question relates to the concept of wave amplitude, which is a fundamental property of waves in physics. The amplitude of a wave is defined as the distance from the equilibrium position to the crest or from the equilibrium to the trough. This distance is the same in both directions, indicating that wave amplitude is uniform and symmetric with respect to the equilibrium position. Hence, in a transverse wave, where particles of the medium move perpendicular to the direction of wave propagation, the distance between the resting position (equilibrium) and the crest is equal to the distance between the resting position and the trough.
Therefore, the correct answer to the question "How does the distance between the resting position and the crest compare with the distance between the resting position and the trough?" is c. The distances are the same.