To determine the coordinates of [tex]\( F' \)[/tex], the image of point [tex]\( F \)[/tex] after the translation, we need to apply the translation rules.
The original coordinates of point [tex]\( F \)[/tex] are [tex]\( (-9, 2) \)[/tex].
The translation involves moving the point 8 units down and 3 units to the right.
1. Translation 3 units to the right:
- When we translate a point to the right by 3 units, we add 3 to its x-coordinate.
- Original [tex]\( x \)[/tex]-coordinate: [tex]\( -9 \)[/tex]
- New [tex]\( x \)[/tex]-coordinate: [tex]\( -9 + 3 = -6 \)[/tex]
2. Translation 8 units down:
- When we translate a point down by 8 units, we subtract 8 from its y-coordinate.
- Original [tex]\( y \)[/tex]-coordinate: [tex]\( 2 \)[/tex]
- New [tex]\( y \)[/tex]-coordinate: [tex]\( 2 - 8 = -6 \)[/tex]
Thus, the new coordinates of point [tex]\( F' \)[/tex] after the translation are [tex]\( (-6, -6) \)[/tex].
Therefore, the correct answer is [tex]\( \boxed{(-6, -6)} \)[/tex].
