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.