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The problem asks to find the distance between two points on a coordinate plane in simplest radical form. To do this, we can use the distance formula:

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

Let me first extract the coordinates of the two points from the graph in the image. I will analyze and then solve the problem based on the points shown.

The coordinates appear to be:
- Point 1: \((-7, 9)\)
- Point 2: \((4, -6)\)

Now, applying the distance formula:

\[
d = \sqrt{(4 - (-7))^2 + (-6 - 9)^2}
\]

Let’s compute this.The distance between the two points \((-7, 9)\) and \((4, -6)\) is approximately 18.60. However, since the problem asks for the distance in simplest radical form, let's simplify the exact radical expression:

\[
d = \sqrt{(4 - (-7))^2 + (-6 - 9)^2} = \sqrt{(11)^2 + (-15)^2} = \sqrt{121 + 225} = \sqrt{346}
\]

The distance in simplest radical form is \( \sqrt{346} \).

Would you like further clarification or details on this solution? Here are some additional related questions:

1. How is the distance formula derived?
2. Can the distance between points ever be negative?
3. How do you find the midpoint between

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

Learn how to find the distance between two points (-7, 9) and (4, -6) on a coordinate plane using the distance formula. The solution is provided in simplest radical form, sqrt(346). This problem is ideal for students in Grades 8-10.

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