3. On a rectangular billiard table $A B C D$, a billiard ball is placed 1 m from corner $D$ and 3 m from corner $C$. The sides of the table are $\overline{A B}=\overline{C D}=4 \mathrm{~m}$ and $\overline{B C}=\overline{A D}=2 \mathrm{~m}$. The ball is struck such that the first bounce is off side $A D$. After three bounces, the ball hits the midpoint of side $C D$. Determine the point on side $A D$ where the ball first bounced.

![](https://cdn.mathpix.com/cropped/2024_06_05_166bcb5a38cc1d401596g-4.jpg?height=396&width=988&top_left_y=571&top_left_x=376)
Solution. The ball is at a distance of $\frac{4}{7} \mathrm{~m}$ from the basket $D$. This follows from the similarity of triangles $M N P$ and $D X P$ (see diagram).