To determine the coordinates of point [tex]\( B \)[/tex] after the translation, we need to follow these steps:
1. Identify the given coordinates of the pre-image of point [tex]\( B \)[/tex]:
- The coordinates are [tex]\( (4, -5) \)[/tex].
2. Understand the translation rule:
- The rule is [tex]\( (x, y) \rightarrow (x + 2, y - 8) \)[/tex].
3. Apply the translation rule to each coordinate:
- For the x-coordinate: [tex]\( x = 4 \)[/tex].
The new x-coordinate after translation will be [tex]\( 4 + 2 = 6 \)[/tex].
- For the y-coordinate: [tex]\( y = -5 \)[/tex].
The new y-coordinate after translation will be [tex]\( -5 - 8 = -13 \)[/tex].
4. Combine the new coordinates:
- After applying the translation, the new coordinates of point [tex]\( B \)[/tex] are [tex]\( (6, -13) \)[/tex].
5. Verify the correct choice from the given options:
- The coordinates corresponding to the choices given are:
- [tex]\( (2, 3) \)[/tex]
- [tex]\( (1, -9) \)[/tex]
- [tex]\( (-3, -4) \)[/tex]
- [tex]\( (6, -13) \)[/tex]
6. Select the correct choice:
- The coordinates [tex]\( (6, -13) \)[/tex] match one of the given options.
Therefore, the coordinates of point [tex]\( B \)[/tex] after the translation are [tex]\( \boxed{(6, -13)} \)[/tex].
