Final answer:
Cepheid variables are extremely useful to astronomers because their absolute magnitude is related directly to their period of pulsation, enabling astronomers to measure their distance based on their period-luminosity relation.
Step-by-step explanation:
The characteristic of Cepheid variables that makes them extremely useful to astronomers is that their absolute magnitude is related directly to their period of pulsation. The longer the period of pulsation, the greater the luminosity of the star. This period-luminosity relation allows astronomers to measure the distance to Cepheid variables by observing their periods and comparing them to their known absolute magnitudes.