Find the distance between the points (-5,-3) and (-9,-8)

To find the distance between two points \((-5, -3)\) and \((-9, -8)\), we use the distance formula:

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

Substituting the coordinates of the points into the formula:

\[
d = \sqrt{((-9) - (-5))^2 + ((-8) - (-3))^2}
\]
\[
d = \sqrt{(-9 + 5)^2 + (-8 + 3)^2}
\]
\[
d = \sqrt{(-4)^2 + (-5)^2}
\]
\[
d = \sqrt{16 + 25}
\]
\[
d = \sqrt{41}
\]
\[
d \approx 6.4
\]

So, the distance between the points is approximately **6.4 units**.

Would you like further explanation or details on the method?

Here are some related questions for you to consider:
1. How do you apply the distance formula in three dimensions?
2. How is the distance formula derived from the Pythagorean theorem?
3. What happens if both points lie on the same axis (horizontal or vertical)?
4. How would you find the midpoint of these two points?
5. How does the distance formula change if we consider spherical coordinates?

**Tip:** Always simplify your expressions before calculating the square root to reduce errors in complex problems.

Learn how to find the distance between two points (-5, -3) and (-9, -8) using the distance formula. This example uses key geometric concepts and the Pythagorean theorem. The final distance is approximately 6.4 units. Suitable for students in Grades 8-10.

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