Transformation of the plane

Let's say you have two points, $A = (1, 2)$ and $B = (5, 6)$.

1. Calculate the distance between A and B.
   Using the distance formula:
   $d = \sqrt{(5 - 1)^2 + (6 - 2)^2}$
   $d = \sqrt{(4)^2 + (4)^2}$
   $d = \sqrt{16 + 16}$
   $d = \sqrt{32}$
   $d = 4\sqrt{2}$ (approximately 5.66 units)

2. Find the midpoint of the line segment AB.
   Using the midpoint formula:
   $M = \left( \frac{1 + 5}{2}, \frac{2 + 6}{2} \right)$
   $M = \left( \frac{6}{2}, \frac{8}{2} \right)$
   $M = (3, 4)$