To determine the length of line \( g'h' \) after translating line \( gh \), we first need to understand that a translation does not change the length of a line segment.
If \( gh \) has a certain length \( d \), the length of \( g'h' \) after the translation will remain \( d \).
Since the problem does not provide the original length of line \( gh \), we cannot calculate the length of \( g'h' \) specifically. However, since the length remains the same after translation, the options provided can be considered:
- 5 units
- 6 units
- 7 units
- 8 units
To find the answer, we need the original length of \( gh \). The translation of 3 units up and 2 units left will not affect the length. Thus, to determine the length \( g'h' \):
- If \( gh \) is not specified lengths or we do not have that information, we would typically need to know it before determining \( g'h' \).
Since the question does not provide enough information regarding the original length of line \( gh \), we would restate that \( g'h' \) is indeed the same length as \( gh \). Therefore, we cannot determine which specific length from the options provided is correct without further context.
If additional information can clarify the initial length of \( gh \), please provide that, and we can conclude accordingly. Otherwise, we confirm that \( g'h' = gh \).