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.