Question

A ball rolls at a $45°$ angle away from one side of the billiard table that has a coordinate grid on it. If the ball starts at the point $\left(0,1\right)$ it will eventually return to its starting point. Would this happen if the ball started from other points on the y-axis between $\left(0,0\right)$ and $\left(0,4\right)$?

Short answer

Yes, the ball will return to its starting point.

Step-by-step solution

Step 1. Given Information.

The starting point is $\left(0,1\right)$ and if the ball started from other points on the y-axis between $\left(0,0\right)\text{and}\left(0,4\right)$.

Step 2. Explanation.

The ball started from other points on the y-axis.

The point is between $\left(0,0\right)\text{and}\left(0,4\right)$.

According to the symmetry, the ball will return to its starting point.

Step 3. Conclusion.

Therefore, the ball will return to its staring point according to the symmetry.