whats the distance between (-3,2) and (-9,8)

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.

Learn how to calculate the distance between the points (-3, 2) and (-9, 8) using the distance formula step-by-step. This problem covers coordinate geometry concepts and the application of the distance formula in calculating distances between points. Suitable for students in Grades 6-8.

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