Line Segment: Length and Center

Line segment has its:

start at $(x_1, y_1)$
end at $(x_2, y_2)$

Length

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

it derives from Pythagorean theorem:

$C^2 = A^2 + B^2$
$|AB|^2 = |AC|^2 + |BC|^2$
$|AB| = \sqrt{|AC|^2 + |BC|^2}$

Center

$$ S = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) $$