To translate line segment CD, which starts at (-1, 1) and ends at (4, 1), 2 units down, we need to subtract 2 from the y-coordinates of both endpoints.
The starting point (-1, 1) is translated to:
\[ (-1, 1 - 2) = (-1, -1) \]
This confirms the starting point of line segment C'D' as (-1, -1).
Now we need to translate the ending point (4, 1):
\[ (4, 1 - 2) = (4, -1) \]
So, the end of line segment C'D' is at the coordinates (4, -1).
Thus, the coordinates for the end of line segment C'D' are:
\[ (4, -1) \]