To determine the coordinates of the point [tex]\( B' \)[/tex] after translation, we start with the pre-image coordinates of point [tex]\( B \)[/tex], which are [tex]\( (4, -5) \)[/tex]. We apply the translation rule [tex]\( (x, y) \rightarrow (x + 2, y - 8) \)[/tex].
Step-by-step process:
1. Translate the x-coordinate:
- The original x-coordinate of point [tex]\( B \)[/tex] is 4.
- According to the translation rule, we add 2 to the x-coordinate: [tex]\( 4 + 2 = 6 \)[/tex].
2. Translate the y-coordinate:
- The original y-coordinate of point [tex]\( B \)[/tex] is -5.
- According to the translation rule, we subtract 8 from the y-coordinate: [tex]\( -5 - 8 = -13 \)[/tex].
Thus, after the translation, the new coordinates of point [tex]\( B' \)[/tex] are [tex]\( (6, -13) \)[/tex].
Among the given options, the coordinates that match our result are:
- [tex]\((2,3)\)[/tex]
- [tex]\((1,-9)\)[/tex]
- [tex]\((-3,-4)\)[/tex]
- [tex]\((6,-13)\)[/tex]
Therefore, the correct answer is:
[tex]\[ (6, -13) \][/tex]
