https://file.aiquickdraw.com/mathbot/file/1730940913058z2iiyykk.jpg

To determine the length of the interval \( AB \), we can use the distance formula between two points:

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

where:
- Point \( A \) has coordinates \( (1, 6) \),
- Point \( B \) has coordinates \( (7, 2) \).

Let's substitute these coordinates into the formula:

\[
AB = \sqrt{(7 - 1)^2 + (2 - 6)^2}
\]
\[
= \sqrt{6^2 + (-4)^2}
\]
\[
= \sqrt{36 + 16}
\]
\[
= \sqrt{52}
\]
\[
= 7.2 \text{ (to 1 decimal place)}
\]

So, the length of the interval \( AB \) is approximately **7.2**.

Would you like further details on the calculation, or do you have any questions?

Here are some related questions to expand understanding:
1. How would you find the length of a line segment between two points in 3D space?
2. What is the general form of the distance formula between two points?
3. How can you verify the accuracy of a calculated distance on a graph?
4. How does the Pythagorean theorem relate to the distance formula?
5. What are some practical applications of calculating distances in coordinate geometry?

**Tip:** Always double-check your coordinates before substituting them into a formula to avoid errors.

Find the length of the interval AB using the coordinates provided in the graph.

Learn how to find the length of the interval AB using the distance formula. This solution involves applying coordinate geometry and the Pythagorean theorem to determine the distance between two points on a plane. Suitable for students in Grades 8-10.

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