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To find the length of the interval \( AB \), we can use the distance formula between two points. The distance formula is:

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

From the graph:
- Point \( A \) is located at \( (-3, 5) \).
- Point \( B \) is located at \( (6, -3) \).

Substitute these coordinates into the formula:

\[
AB = \sqrt{(6 - (-3))^2 + (-3 - 5)^2}
\]

Simplify each part of the equation:

1. \( x_2 - x_1 = 6 - (-3) = 6 + 3 = 9 \)
2. \( y_2 - y_1 = -3 - 5 = -8 \)

Now square these results:

\[
AB = \sqrt{(9)^2 + (-8)^2} = \sqrt{81 + 64} = \sqrt{145}
\]

So, the length of \( AB \) is:

\[
AB = \sqrt{145} \approx 12.04
\]

Therefore, \( AB \approx 12.04 \) units.

Would you like more details or have any further questions?

Here are some related questions you might find interesting:

1. How would you calculate the midpoint of the interval \( AB \)?
2. What would change in the calculation if point \( B \) were at \( (6, 3) \)?
3. How do you interpret the distance formula geometrically?
4. Can the distance formula be applied in three-dimensional space, and if so, how?
5. What is the significance of the sign of coordinates in distance calculations?

**Tip:** Remember, when using the distance formula, always square the differences in coordinates to avoid any negative impact on the calculation, as distance is always non-negative.

Learn how to find the length of the interval AB using the distance formula in coordinate geometry. This problem provides a step-by-step solution for calculating the distance between points A(-3,5) and B(6,-3), covering essential concepts suitable for students in Grades 9-10.

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