https://file.aiquickdraw.com/mathbot/file/17292796141087542a9bt.jpg

The image shows a coordinate plane with three points that form a triangle, representing Samuel's running path. We can calculate the total distance Samuel ran by finding the distances between each pair of points and summing them up. The points on the graph appear to be approximately:

- Point 1: (-5, 8)
- Point 2: (4, 6)
- Point 3: (1, -4)

### Steps to find the total distance:

1. **Distance between (-5, 8) and (4, 6)**:
   Using the distance formula:
   \[
   d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
   \]
   Substituting the coordinates:
   \[
   d = \sqrt{(4 - (-5))^2 + (6 - 8)^2} = \sqrt{(9)^2 + (-2)^2} = \sqrt{81 + 4} = \sqrt{85} \approx 9.22 \, \text{units}
   \]

2. **Distance between (4, 6) and (1, -4)**:
   \[
   d = \sqrt{(1 - 4)^2 + (-4 - 6)^2} = \sqrt{(-3)^2 + (-10)^2} = \sqrt{9 + 100} = \sqrt{109} \approx 10.44 \, \text{units}
   \]

3. **Distance between (1, -4) and (-5, 8)**:
   \[
   d = \sqrt{(-5 - 1)^2 + (8 - (-4))^2} = \sqrt{(-6)^2 + (12)^2} = \sqrt{36 + 144} = \sqrt{180} \approx 13.42 \, \text{units}
   \]

### Total Distance:
\[
\text{Total Distance} \approx 9.22 + 10.44 + 13.42 = 33.08 \, \text{units}
\]
Therefore, the closest answer to this value is **A: 39 units**.

Would you like a more detailed explanation, or do you have any questions about this process?

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Here are five related questions you might want to explore:
1. How is the distance formula derived from the Pythagorean theorem?
2. What is the significance of using coordinate geometry to calculate distances?
3. How would the total distance change if the points were closer together?
4. How can you calculate the perimeter of irregular shapes using coordinates?
5. How do you calculate the distance between two points in three-dimensional space?

**Tip:** Always double-check your coordinates before applying the distance formula to ensure accuracy.

Samuel went on a run in the park. His path is shown on the coordinate plane. What is the total distance Samuel ran?

Learn how to calculate the total distance Samuel ran on a coordinate plane using the distance formula and the Pythagorean theorem. This problem involves key concepts in coordinate geometry and is suitable for students in Grades 7-9.

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