To find the distance between points $A$ and $B$ on the graph, we’ll use the distance formula:

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

Step-by-Step Solution:

1. Identify Coordinates of Points $A$ and $B$:

   • Point $A$ is at $(5, 3)$.
   • Point $B$ is at $(-4, -4)$.

2. Substitute into the Distance Formula: $d = \sqrt{(5 - (-4))^2 + (3 - (-4))^2}$ Simplify inside the parentheses: $d = \sqrt{(5 + 4)^2 + (3 + 4)^2}$ $d = \sqrt{9^2 + 7^2}$

3. Calculate Each Square: $d = \sqrt{81 + 49}$ $d = \sqrt{130}$

4. Take the Square Root: $d \approx 11.4$

Final Answer:

The distance traveled by the object is approximately 11.4 miles.

Would you like more details on this solution, or do you have any questions?

Here are five related questions to deepen understanding:

1. How would the calculation change if point $B$ were at $(-4, 4)$ instead of $(-4, -4)$?
2. What is the midpoint between points $A$ and $B$?
3. How do you determine the slope of the line segment connecting $A$ and $B$?
4. If the object took 2 hours to travel from $A$ to $B$, what would be its average speed?
5. How can you use the Pythagorean theorem to check this distance?

Tip: Remember that the distance formula is based on the Pythagorean theorem, which is why it's perfect for calculating distances in coordinate geometry.