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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!

Find the exact distance between the points (-7, -2) and (-3, -4).

Learn how to calculate the exact distance between two points (-7, -2) and (-3, -4) using the distance formula. This step-by-step solution involves applying key concepts from coordinate geometry and the Pythagorean Theorem. Ideal for high school students.

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