To find the coordinates of [tex]\( F' \)[/tex] after translating point [tex]\( F \)[/tex], we follow these steps carefully:
1. Identify the original coordinates: The coordinates of the pre-image of point [tex]\( F \)[/tex] are given as [tex]\((-9, 2)\)[/tex].
2. Determine the translation values:
- The point is translated 3 units to the right, which affects the x-coordinate.
- The point is translated 8 units down, which affects the y-coordinate.
3. Apply the translation to the x-coordinate:
- Moving 3 units to the right increases the x-coordinate. This means we add 3 to the original x-coordinate.
[tex]\[
x' = -9 + 3 = -6
\][/tex]
4. Apply the translation to the y-coordinate:
- Moving 8 units down decreases the y-coordinate. This means we subtract 8 from the original y-coordinate.
[tex]\[
y' = 2 - 8 = -6
\][/tex]
5. Combine the new coordinates: After applying the translations, the new coordinates of [tex]\( F' \)[/tex] are [tex]\((-6, -6)\)[/tex].
Thus, the coordinates of [tex]\( F' \)[/tex] are [tex]\(\boxed{(-6, -6)}\)[/tex].
