Points A, B, and C are represented on a Cartesian plane. Given the coordinates of A as (2; -1) and C as (5; 3), determine the coordinates of B and the lengths of line segments AB and BC.

Point B is directly below point C and horizontally aligned with point A.
This means the x-coordinate of B is the same as the x-coordinate of C, and the y-coordinate of B is the same as the y-coordinate of A.

Given $A = (2; -1)$ and $C = (5; 3)$.
The x-coordinate of B is $C_x = 5$.
The y-coordinate of B is $A_y = -1$.
So, the coordinates of B are $(5; -1)$.

B: $\boxed{(5; -1)}$

1.3.2 Write down the lengths of AB and BC.

AB is a horizontal line segment. Its length is the absolute difference of the x-coordinates of A and B.
$A = (2; -1)$
$B = (5; -1)$

BC is a vertical line segment. Its length is the absolute difference of the y-coordinates of B and C.
$B = (5; -1)$
$C = (5; 3)$

AB: $\boxed{3}$
BC: $\boxed{4}$