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To find the distance between the two points on the coordinate plane, we will use the **distance formula**, which is:

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

Let's extract the coordinates from the graph:

1. The first point is approximately \((-3, 7)\).
2. The second point is approximately \((-6, -9)\).

Now, plug these values into the distance formula:

\[
d = \sqrt{((-6) - (-3))^2 + ((-9) - (7))^2}
\]

Let’s calculate this step by step:

\[
d = \sqrt{(-6 + 3)^2 + (-9 - 7)^2}
\]
\[
d = \sqrt{(-3)^2 + (-16)^2}
\]
\[
d = \sqrt{9 + 256}
\]
\[
d = \sqrt{265}
\]

The distance between the two points in simplest radical form is \(\sqrt{265}\).

Would you like more details on this solution? 

Here are some related questions:
1. What are some real-life applications of the distance formula?
2. How do you calculate the distance between points in 3D space?
3. Can you prove the distance formula geometrically using the Pythagorean Theorem?
4. How would the formula change if the points were given in polar coordinates?
5. What is the midpoint formula, and how is it related to the distance formula?

**Tip:** Always simplify radical expressions as much as possible, and check if perfect square factors exist within the radicand!

Find the distance between the two points in simplest radical form.

Learn how to calculate the distance between two points using the distance formula, derived from the Pythagorean Theorem, with a detailed step-by-step solution. This problem covers key concepts in coordinate geometry, making it suitable for high school students.

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