To find the coordinates of [tex]\(F'\)[/tex] after a translation, we need to apply the given translation to the coordinates of the pre-image of point [tex]\(F\)[/tex].
1. Initial Coordinates: The coordinates of the pre-image of point [tex]\(F\)[/tex] are [tex]\((-9, 2)\)[/tex].
2. Translation Details: The hexagon is translated 3 units to the right and 8 units down.
3. Calculating the New Coordinates:
- To move a point 3 units to the right, we add 3 to the x-coordinate.
- To move a point 8 units down, we subtract 8 from the y-coordinate.
4. Step-by-Step Calculation:
- Original x-coordinate: [tex]\(-9\)[/tex]
- After moving right by 3 units: [tex]\(-9 + 3 = -6\)[/tex]
- Original y-coordinate: [tex]\(2\)[/tex]
- After moving down by 8 units: [tex]\(2 - 8 = -6\)[/tex]
5. New Coordinates: After applying the translation, the new coordinates of [tex]\(F'\)[/tex] are [tex]\((-6, -6)\)[/tex].
Thus, the coordinates of [tex]\(F'\)[/tex] are [tex]\((-6, -6)\)[/tex].
Therefore, the correct answer is:
[tex]\[
(-6, -6)
\][/tex]
