To solve the problem of finding the distance between the two points $A$ and $B$ as shown in the image, we use the distance formula:

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

Step-by-step solution:

1. Identify coordinates of points $A$ and $B$:

   • $A(-2, -4)$
   • $B(4, -3)$

2. Substitute into the distance formula: $\text{Distance} = \sqrt{(4 - (-2))^2 + (-3 - (-4))^2}$

3. Simplify the differences: $\text{Distance} = \sqrt{(4 + 2)^2 + (-3 + 4)^2}$ $\text{Distance} = \sqrt{6^2 + 1^2}$

4. Square the values: $\text{Distance} = \sqrt{36 + 1}$ $\text{Distance} = \sqrt{37}$

5. Compute the square root and round to 2 decimal places: $\text{Distance} \approx 6.08$

Final Answer:

$\text{Distance} = 6.08$

Would you like a more detailed explanation or have questions?
Here are 5 related questions for exploration:

1. What is the purpose of the distance formula in coordinate geometry?
2. How does the Pythagorean theorem relate to the distance formula?
3. Can this distance formula be extended to three-dimensional space?
4. How would the distance change if one point were shifted closer to the origin?
5. Why is rounding necessary in real-world applications?

Tip: When solving geometry problems, always double-check the coordinates to avoid errors!