To find the distance between Truth Park and the mall, we can use the distance formula. The distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a coordinate plane is given by:

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

Step 1: Determine the coordinates of the mall and Truth Park relative to the city center.

• The mall is 3 miles west and 4 miles south of the city center, so its coordinates relative to the center are $(-3, -4)$.
• Truth Park is 3 miles east and 2 miles north of the city center, so its coordinates relative to the center are $(3, 2)$.

Step 2: Apply the distance formula.

Using the coordinates for the mall $(-3, -4)$ and Truth Park $(3, 2)$, we calculate:

$d = \sqrt{(3 - (-3))^2 + (2 - (-4))^2}$

Simplify inside the parentheses:

$d = \sqrt{(3 + 3)^2 + (2 + 4)^2}$

$d = \sqrt{6^2 + 6^2}$

$d = \sqrt{36 + 36}$

$d = \sqrt{72}$

Step 3: Simplify and find the distance.

$d = \sqrt{72} \approx 8.5 \text{ miles}$

So, the distance from Truth Park to the mall is approximately $\mathbf{8.5}$ miles.

Would you like further explanation or have any questions?

Here are some related questions:

1. How do you calculate the distance between two points in three-dimensional space?
2. What is the significance of the distance formula in real-world applications?
3. How would you find the midpoint of the segment connecting the mall and Truth Park?
4. How can you determine the coordinates of a point that divides a segment in a given ratio?
5. How would the distance change if the coordinates were given on a different scale?

Tip: When dealing with distances, always double-check your signs and operations inside the square root to ensure accuracy.