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The problem asks to find the distance between two points, \( A \) and \( B \), based on their positions in the graph.

We can use the **distance formula** to calculate the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\):

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

### Step-by-step solution:
1. **Identify coordinates**: From the graph, the coordinates of the points \( A \) and \( B \) appear to be:
   - \( A(x_1, y_1) = (1, 1) \)
   - \( B(x_2, y_2) = (6, 5) \)

2. **Apply the distance formula**:
\[
d = \sqrt{(6 - 1)^2 + (5 - 1)^2} = \sqrt{5^2 + 4^2} = \sqrt{25 + 16} = \sqrt{41}
\]

3. **Approximate the result**:
\[
d \approx 6.4
\]

Thus, the distance between points \( A \) and \( B \) is approximately **6.4 units**.

Let me know if you need further details!

### Related questions:
1. How do we calculate the midpoint between two points?
2. What is the distance formula used for in real-life applications?
3. How would the distance change if the points were in 3D space?
4. Can we apply the Pythagorean Theorem in this situation?
5. What is the difference between calculating distance on a grid versus in a continuous space?

### Tip:
Always double-check the coordinates from a graph or diagram to ensure accuracy when applying formulas!

Find the distance between points A and B on the graph, and round the answer to the nearest tenth.

Learn how to calculate the distance between two points A and B on a graph using the distance formula. This problem involves key concepts from coordinate geometry and the Pythagorean Theorem, suitable for students in Grades 7-10.

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