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To find the distance between two points, we can use the distance formula:

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

From the graph, let's identify the coordinates of the two points:

- The first point is at approximately \((-2, -9)\).
- The second point is at approximately \((7, 5)\).

Now, let's apply the distance formula:

\[
d = \sqrt{(7 - (-2))^2 + (5 - (-9))^2}
\]

Let me calculate this for you.The distance between the two points is approximately \( 16.64 \). However, in simplest radical form, we can further simplify it.

Let's break down the calculation:

\[
d = \sqrt{(7 - (-2))^2 + (5 - (-9))^2} = \sqrt{9^2 + 14^2} = \sqrt{81 + 196} = \sqrt{277}
\]

Thus, the exact distance between the two points in simplest radical form is \( \sqrt{277} \).

Would you like more details or have any questions? Here are some related questions for further exploration:

1. What is the distance formula derived from?
2. Can you find the midpoint between these two points?
3. How can you estimate \(\sqrt{277}\) more precisely?
4. What is the significance of radical form in mathematics?
5. How would the distance change if the points were shifted in the graph?

**Tip:** Always simplify square roots for exact answers in radical form when possible.

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

Discover how to calculate the distance between two points using the distance formula derived from the Pythagorean theorem. This guide provides a step-by-step solution with exact answers in simplest radical form. Ideal for high school students in grades 9 to 12.

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