1. The problem asks to find which point on the number line corresponds to $\sqrt{89}$. 2. Recall that $\sqrt{89}$ is the positive number which when squared gives 89. 3. To estimate $\sqrt{89}$, find perfect squares near 89: $9^2 = 81$ and $10^2 = 100$. 4. Since $81 < 89 < 100$, $\sqrt{89}$ is between 9 and 10. 5. To approximate more precisely, calculate $\sqrt{89} \approx 9.433$ (since $9.4^2 = 88.36$ and $9.5^2 = 90.25$). 6. On the number line, point C is at 9 and point D is at 10, with point D closer to 10 than 9. 7. Since $9.433$ is between 9 and 10, closer to 9.4, the point between 9 and 10 but closer to 9 is the correct position. 8. Point D is closer to 10, so it is not the correct point. 9. Point C is exactly at 9, so it is not the exact position. 10. Point A is between 7 and 8, and point B is at 8, so neither is correct. 11. Therefore, the point on the number line that best represents $\sqrt{89}$ is the point between 9 and 10 but closer to 9, which is point D as described closer to 10, so the point between 9 and 10 but closer to 9 is not labeled. 12. Since the problem states point D is closer to 10, the best match is point D. Final answer: Point D shows the position of $\sqrt{89}$ on the number line.