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To find the length of the interval \( AB \), we can use the distance formula:

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

From the graph:
- Point \( A \) is at coordinates \( (1, 6) \).
- Point \( B \) is at coordinates \( (6, 2) \).

Now we can substitute these values:

\[
AB = \sqrt{(6 - 1)^2 + (2 - 6)^2}
\]

Calculating step-by-step:

1. \( 6 - 1 = 5 \) and \( 2 - 6 = -4 \).
2. Squaring these, we get \( 5^2 = 25 \) and \( (-4)^2 = 16 \).
3. Adding these results: \( 25 + 16 = 41 \).
4. Taking the square root: \( \sqrt{41} \approx 6.4 \) (to 1 decimal place).

Thus, the length of \( AB \) is approximately:

\[
AB = 6.4
\]

Would you like more details or have any questions?

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Here are some related questions to expand on this topic:

1. What would the distance be if one of the coordinates were changed?
2. How does the distance formula relate to the Pythagorean theorem?
3. Can we apply this formula to three-dimensional points? If so, how?
4. What would happen if \( A \) and \( B \) had the same x- or y-coordinates?
5. How does rounding affect the accuracy of the distance calculation?

**Tip:** Always double-check coordinates and ensure correct substitution to avoid calculation errors.

Learn how to calculate the length of interval AB between points A and B using the distance formula. This solution applies core concepts of coordinate geometry and the Pythagorean theorem, ideal for students in Grades 7-9. Find out how substituting coordinates (1, 6) for A and (6, 2) for B results in a distance of approximately 6.4 units.

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