https://file.aiquickdraw.com/mathbot/file/1730222328958w250dvzq.jpg

To find the distance the object traveled from point \( A \) to point \( B \) on the graph, we can use the **distance formula** between two points in a coordinate plane. The formula is:

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

### Step 1: Identify Coordinates of Points \( A \) and \( B \)
From the graph:
- Point \( A \) has coordinates \( (-5, -5) \).
- Point \( B \) has coordinates \( (4, 3) \).

### Step 2: Substitute the Values into the Distance Formula
Using \( (x_1, y_1) = (-5, -5) \) and \( (x_2, y_2) = (4, 3) \):

\[
d = \sqrt{(4 - (-5))^2 + (3 - (-5))^2}
\]
\[
= \sqrt{(4 + 5)^2 + (3 + 5)^2}
\]
\[
= \sqrt{(9)^2 + (8)^2}
\]
\[
= \sqrt{81 + 64}
\]
\[
= \sqrt{145}
\]

### Step 3: Calculate and Round the Distance
\[
d \approx 12.0
\]

### Final Answer:
The distance the object traveled is approximately **12.0 miles**.

Would you like more details on any steps or have any questions?

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Here are five related questions for further exploration:
1. How would the distance change if the coordinates of point \( A \) or \( B \) were altered slightly?
2. How do we interpret the distance formula in terms of the Pythagorean theorem?
3. What would happen if each grid square represented 0.5 miles instead of 1 mile?
4. How can we find the midpoint between points \( A \) and \( B \)?
5. Can this distance formula be extended to three-dimensional space?

**Tip:** Always double-check coordinate values when reading from a graph to ensure accuracy in calculations.

An object begins at point A and moves to point B. How far did the object travel? Round your answer to one decimal place.

Learn how to calculate the distance between two points, A and B, on a coordinate plane using the distance formula. This problem explores coordinate geometry concepts and the Pythagorean theorem. Suitable for students in Grades 8-10.

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