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To calculate the length of segment \( AB \), we can use the distance formula between two points in the coordinate plane, which is:

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

Here, the coordinates of \( A \) are \( (8, 2) \), and the coordinates of \( B \) are \( (2, 10) \). Plugging these values into the distance formula:

\[
d = \sqrt{(2 - 8)^2 + (10 - 2)^2}
\]
\[
d = \sqrt{(-6)^2 + (8)^2}
\]
\[
d = \sqrt{36 + 64}
\]
\[
d = \sqrt{100}
\]
\[
d = 10
\]

So, the length of segment \( AB \) is \( 10 \) units.

Would you like more details or have any questions?

### Related Questions:
1. How do you derive the distance formula from the Pythagorean theorem?
2. How would the calculation change if the coordinates were in 3D space?
3. Can the midpoint of segment \( AB \) also be calculated?
4. What are some practical applications of finding distances between points in geometry?
5. How does the distance formula relate to vectors in linear algebra?

**Tip:** The distance formula is essentially the Pythagorean theorem applied to the difference in x and y coordinates of two points in the plane.

The coordinates of A are (8, 2), and the coordinates of B are (2, 10). What is the length of segment AB?

Learn how to calculate the length of segment AB between points A(8, 2) and B(2, 10) using the distance formula. This problem is suitable for middle school students and introduces key geometry concepts and the Pythagorean theorem.

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