To determine the coordinates of [tex]\( F' \)[/tex] after the translation, follow these steps:
1. Identify the initial coordinates of point [tex]\( F \)[/tex]: The coordinates are given as [tex]\( (-9, 2) \)[/tex].
2. Understand the translation directions:
- Rightward translation: Moving a point 3 units to the right implies adding 3 to the x-coordinate.
- Downward translation: Moving a point 8 units down implies subtracting 8 from the y-coordinate.
3. Apply the translation to the x-coordinate:
- Initially, the x-coordinate of point [tex]\( F \)[/tex] is [tex]\( -9 \)[/tex].
- Adding 3 units to the right: [tex]\( -9 + 3 = -6 \)[/tex].
4. Apply the translation to the y-coordinate:
- Initially, the y-coordinate of point [tex]\( F \)[/tex] is [tex]\( 2 \)[/tex].
- Subtracting 8 units down: [tex]\( 2 - 8 = -6 \)[/tex].
5. Determine the new coordinates of [tex]\( F' \)[/tex]:
- After translating 3 units to the right and 8 units down, the new coordinates of [tex]\( F' \)[/tex] are [tex]\( (-6, -6) \)[/tex].
Thus, the coordinates of [tex]\( F' \)[/tex] are [tex]\( (-6, -6) \)[/tex].
So, the correct answer is [tex]\( \boxed{(-6, -6)} \)[/tex].
