Is the official correct in continuing the 10 second count when B-1 bats the ball away from A-1 while A-1 is dribbling in the backcourt?

The official is correct in continuing the 10-second count because team A, represented by player A-1, is still considered to have control of the ball. In basketball, control of the ball is defined as having possession, which means that the player is actively dribbling or holding the ball. In this scenario, even though B-1 has batted the ball away, it does not equate to the loss of control by A-1 until the situation clearly indicates that A-1 has lost the ability to dribble or maintain possession.

Continuing the 10-second count is important because the rule dictates that the offensive team (team A) has 10 seconds to advance the ball past half-court while maintaining possession. Since A-1 was actively dribbling and the ball was still in A-1's area of control, the count must continue until A-1 either loses control of the ball completely or successfully crosses half-court within the allotted time.

The other options suggest scenarios in which the count would stop or would only continue under specific conditions. However, none of those situations apply here since control by A-1 is still present, thus validating the continuation of the 10-second count.