To find the distance between the points $(-4, 5)$ and $(-9, -7)$, we use the distance formula:

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

Substituting the given points into the formula:

$\text{Distance} = \sqrt{((-9) - (-4))^2 + ((-7) - 5)^2}$

Simplify the expression inside the square root:

$\text{Distance} = \sqrt{(-9 + 4)^2 + (-7 - 5)^2} = \sqrt{(-5)^2 + (-12)^2}$

Calculate the squares:

$\text{Distance} = \sqrt{25 + 144} = \sqrt{169}$

Finally, take the square root:

$\text{Distance} = 13$

So, the distance between the points $(-4, 5)$ and $(-9, -7)$ is 13 units.

Would you like more details or have any questions?

Here are 5 related questions:

1. How can the distance formula be used in three-dimensional space?
2. What is the midpoint between the points $(-4, 5)$ and $(-9, -7)$?
3. What is the equation of the line passing through the points $(-4, 5)$ and $(-9, -7)$?
4. How do you calculate the distance between two points using vectors?
5. What would be the distance if the points were $(-4, -5)$ and $(-9, 7)$?

Tip: When working with negative coordinates, be careful with signs when performing subtraction in the distance formula.