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?

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.