To find the distance between the points $(-3, 2)$ and $(-9, 8)$, you can use the distance formula:

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

Here, $(x_1, y_1) = (-3, 2)$ and $(x_2, y_2) = (-9, 8)$. Plugging in the values:

$d = \sqrt{(-9 - (-3))^2 + (8 - 2)^2}$

Simplifying further:

$d = \sqrt{(-9 + 3)^2 + (8 - 2)^2}$ $d = \sqrt{(-6)^2 + (6)^2}$ $d = \sqrt{36 + 36}$ $d = \sqrt{72}$

Simplifying $\sqrt{72}$ gives:

$d = \sqrt{36 \times 2} = 6\sqrt{2}$

So, the distance between the points $(-3, 2)$ and $(-9, 8)$ is $6\sqrt{2}$.

Would you like more details or have any questions about this solution?

Here are 5 related questions you might find interesting:

1. How can you simplify the square root of a non-perfect square?
2. What is the distance between the points $(1, 1)$ and $(7, 7)$?
3. How do you calculate the distance between a point and a line in a coordinate plane?
4. How can you determine if three points are collinear using distances?
5. How do you find the area of a triangle given its vertices in the coordinate plane?

Tip: When calculating distances, it’s often useful to simplify square roots by factoring out perfect squares to make the answer more manageable.