To solve this problem, we need to apply the given translation rule to the coordinates of point B. The rule we are given is [tex]\((x, y) \rightarrow (x + 2, y - 8)\)[/tex].
Step-by-step, here's how we proceed:
1. Start with the given coordinates of point B, which are [tex]\((4, -5)\)[/tex].
2. Apply the translation rule:
- For the x-coordinate: [tex]\(x + 2 = 4 + 2\)[/tex]
- For the y-coordinate: [tex]\(y - 8 = -5 - 8\)[/tex]
3. Perform the calculations:
- [tex]\(4 + 2 = 6\)[/tex]
- [tex]\(-5 - 8 = -13\)[/tex]
So, after applying the translation, the new coordinates of [tex]\(B^\prime\)[/tex] are [tex]\((6, -13)\)[/tex].
Therefore, the coordinates of [tex]\(B^\prime\)[/tex] are [tex]\((6, -13)\)[/tex], so the correct choice is:
[tex]\((6, -13)\)[/tex].
