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To find the length of the interval \( AB \) between points \( A \) and \( B \) on the coordinate plane, we can use the distance formula:

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

From the image:
- Point \( A \) has coordinates \( (2, 2) \).
- Point \( B \) has coordinates \( (6, 5) \).

Substitute these values into the formula:
\[
AB = \sqrt{(6 - 2)^2 + (5 - 2)^2}
\]

Calculate step-by-step:
1. \( 6 - 2 = 4 \) and \( 5 - 2 = 3 \).
2. Square these results: \( 4^2 = 16 \) and \( 3^2 = 9 \).
3. Add the squares: \( 16 + 9 = 25 \).
4. Take the square root: \( \sqrt{25} = 5 \).

So, the length of the interval \( AB \) is:
\[
AB = 5
\]

Would you like further details on this solution or have any other questions?

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Here are five related questions to deepen understanding:
1. What is the distance formula, and why does it work for finding the length between two points?
2. How would the length of \( AB \) change if point \( B \) were at \( (6, 6) \)?
3. What is the midpoint of the line segment \( AB \) with points \( A \) at \( (2, 2) \) and \( B \) at \( (6, 5) \)?
4. How can the distance formula be derived from the Pythagorean theorem?
5. How would you calculate the distance between two points in three-dimensional space?

**Tip:** Always double-check the coordinates before substituting them into the distance formula to avoid simple errors.

Learn how to find the length of the interval AB on a coordinate plane with points A at (2, 2) and B at (6, 5). This guide uses the distance formula and applies the Pythagorean Theorem for a clear step-by-step solution. Ideal for students in Grades 6-8.

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