The phrase "moved to and fro" refers to a motion of going back and forth repeatedly. Its antonyms, on the other hand, refer to movements that are steady and continuous. One antonym is "stationary," which means still or not moving. Another is "fixed," which means securely held in place. "Immobile" is another antonym, which means unable to move. "Stable" is an antonym that means firm, unwavering, and consistent. These antonyms all imply a sense of stillness, composure, and steadiness, which are the opposite of the restless, erratic movements that "moved to and fro" connotes.