To find the exact distance between the points $(-7, -2)$ and $(-3, -4)$, we can use the distance formula:

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

Where:

• $(x_1, y_1)$ is $(-7, -2)$
• $(x_2, y_2)$ is $(-3, -4)$

Substituting the coordinates into the formula:

$d = \sqrt{(-3 - (-7))^2 + (-4 - (-2))^2}$ $d = \sqrt{(-3 + 7)^2 + (-4 + 2)^2}$ $d = \sqrt{(4)^2 + (-2)^2}$ $d = \sqrt{16 + 4}$ $d = \sqrt{20}$ $d = 2\sqrt{5}$

So, the exact distance between the points is $2\sqrt{5}$.

Would you like a deeper explanation, or do you have any other questions?

Here are some related questions:

1. How do you derive the distance formula from the Pythagorean Theorem?
2. What are the properties of a distance function in geometry?
3. Can you apply the distance formula to points in three dimensions?
4. What is the midpoint between $(-7, -2)$ and $(-3, -4)$?
5. How would you find the slope of the line through these two points?

Tip: Always double-check signs when working with negative coordinates in formulas!