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To solve this problem, we need to determine the total distance traveled by the ball, which consists of two parts:

1. The distance from the **pitcher** to the **batter**.
2. The distance from the **batter** to the **shortstop**.

### Step 1: Determine the coordinates
The units on the grid represent a distance of 9 feet for each grid unit. Let's find the coordinates of the **pitcher**, **batter**, and **shortstop**.

- **Pitcher**: Looking at the grid, the pitcher is at \( (5, 5) \).
- **Batter**: The batter is positioned at \( (2, 2) \).
- **Shortstop**: The shortstop is located at \( (8, 10) \).

### Step 2: Calculate the distances
We will use the distance formula to calculate the distance between each pair of points. The distance formula between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

#### Distance from the pitcher to the batter:
Using the coordinates of the pitcher \( (5, 5) \) and the batter \( (2, 2) \), we have:
\[
d_1 = \sqrt{(5 - 2)^2 + (5 - 2)^2} = \sqrt{3^2 + 3^2} = \sqrt{9 + 9} = \sqrt{18}
\]
\[
d_1 = 4.24 \text{ units}
\]
Converting this into feet:
\[
d_1 = 4.24 \times 9 = 38.16 \text{ feet}
\]

#### Distance from the batter to the shortstop:
Using the coordinates of the batter \( (2, 2) \) and the shortstop \( (8, 10) \), we have:
\[
d_2 = \sqrt{(8 - 2)^2 + (10 - 2)^2} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100}
\]
\[
d_2 = 10 \text{ units}
\]
Converting this into feet:
\[
d_2 = 10 \times 9 = 90 \text{ feet}
\]

### Step 3: Total distance traveled
The total distance is the sum of \( d_1 \) and \( d_2 \):
\[
\text{Total distance} = 38.16 + 90 = 128.16 \text{ feet}
\]
Rounding to the nearest tenth:
\[
\boxed{128.2 \text{ feet}}
\]

Let me know if you'd like a more detailed breakdown or further explanations. 

Here are 5 related questions you can try:
1. What is the distance from the pitcher to the first baseman?
2. How would the answer change if each unit were 10 feet instead of 9 feet?
3. Can you find the midpoint between the batter and the shortstop?
4. What is the slope of the line connecting the pitcher and the batter?
5. How much time would it take for the ball to reach the shortstop if it traveled at a speed of 60 feet per second?

**Tip**: When using the distance formula, always check that you are using the correct coordinates for each point to avoid mistakes.

A pitcher throws a ball to a batter, who hits the ball to the shortstop. If the ball travels in a straight line between each, what is the total distance traveled by the ball? Round your answer to the nearest tenth of a foot.

Solve this geometry problem to find the total distance traveled by a baseball from the pitcher to the batter and then to the shortstop. Learn to apply the distance formula and round your answer to the nearest tenth of a foot. Suitable for students in Grades 7-9.

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