https://file.aiquickdraw.com/mathbot/file/1725503983323en2sl0kq.jpg

To help you find the distance between the two points on the graph in the image, I will use the distance formula. The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a coordinate plane is given by:

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

Let me inspect the image and determine the coordinates of the two points.From the image, I can identify the approximate coordinates of the two points on the graph:

- The first point appears to be at \((-3, 2)\).
- The second point seems to be at \((2, -3)\).

Now, applying the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
\[
d = \sqrt{(2 - (-3))^2 + (-3 - 2)^2}
\]
\[
d = \sqrt{(2 + 3)^2 + (-3 - 2)^2}
\]
\[
d = \sqrt{5^2 + (-5)^2}
\]
\[
d = \sqrt{25 + 25} = \sqrt{50}
\]
\[
d = 5\sqrt{2}
\]

So, the distance between the two points in simplest radical form is \(5\sqrt{2}\).

Do you want more details or have any questions?

Here are five relative questions to deepen understanding:
1. How is the distance formula derived from the Pythagorean theorem?
2. How would the distance formula change in three dimensions?
3. Can the midpoint between these two points also be found?
4. How does the distance formula relate to the slope of a line between the points?
5. How would this problem differ if asked in a polar coordinate system?

**Tip:** Always check your points’ coordinates carefully from graphs to ensure accuracy before applying formulas.

Find the distance between two points in simplest radical form.

Learn how to find the distance between two points using the distance formula, applied to the points (-3, 2) and (2, -3). This step-by-step solution simplifies the result to the radical form 5√2, making it perfect for Grades 9-10 students.

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