To find the distance between points \( P(5, -8) \) and \( Q(-3, -7) \), we can use the distance formula:

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

Here, \((x_1, y_1) = (5, -8)\) and \((x_2, y_2) = (-3, -7)\).

Now, plug in the values:

\[
\text{Distance} = \sqrt{((-3) - 5)^2 + ((-7) - (-8))^2}
\]

Simplify the expression:

\[
\text{Distance} = \sqrt{(-8)^2 + (1)^2} = \sqrt{64 + 1} = \sqrt{65}
\]

So, the distance between the points \( P \) and \( Q \) is \(\sqrt{65}\) units.

Would you like further details or have any questions? 

Here are 5 related questions to expand your understanding:
1. How do you find the midpoint between two points?
2. What is the formula for the slope of a line between two points?
3. How do you determine if two points lie on the same line?
4. Can you calculate the area of a triangle given three points?
5. What is the distance between two points in 3D space?

**Tip:** When working with distances or lengths in geometry, always check if you can simplify square roots to their simplest form.

Learn how to calculate the distance between points (5, -8) and (-3, -7) using the distance formula. This problem covers coordinate geometry, specifically the distance formula for finding distances between two points on a plane. Suitable for students in Grades 7-9.

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