6. Aim Julio is playing a game where he rolls a ball from one corner of the room to the opposite corner, without touching the walls. In how many different directions could Julio roll the ball to reach its target? How do you know?

To determine the number of different directions Julio could roll the ball to reach the opposite corner of the room, we can think of the problem in terms of geometry and movement in a two-dimensional space. Assuming the room is rectangular, Julio starts at one corner (let's say the bottom-left corner) and needs to reach the opposite corner (the top-right corner). The ball can be rolled in any direction that leads towards the target corner without touching the walls. 1. **Understanding the Directions**: The ball can be rolled in any direction that is a straight line towards the target corner. This means that the ball can be rolled at any angle from the starting corner to the target corner. 2. **Infinite Directions**: Since there are infinitely many angles between the two corners (from 0 degrees to 360 degrees), Julio can roll the ball in an infinite number of directions. 3. **Conclusion**: Therefore, the answer is that Julio can roll the ball in infinitely many different directions to reach the opposite corner of the room. In summary, the number of different directions Julio could roll the ball is infinite, as he can choose any angle between the two corners.