Sure! To solve this problem, we'll take the given pre-image coordinates of point B and apply the translation rule step-by-step.
The initial coordinates of point B are given as (4, -5).
The translation rule provided is:
[tex]\[
(x, y) \rightarrow (x+2, y-8)
\][/tex]
This means:
- We need to add 2 to the x-coordinate.
- We need to subtract 8 from the y-coordinate.
Let's apply the rule to the given point:
1. Start with the x-coordinate:
- Original x-coordinate: [tex]\(4\)[/tex]
- Apply the translation: [tex]\(4 + 2 = 6\)[/tex]
2. Now for the y-coordinate:
- Original y-coordinate: [tex]\(-5\)[/tex]
- Apply the translation: [tex]\(-5 - 8 = -13\)[/tex]
Therefore, after applying the translation rule, the new coordinates of point [tex]\(B'\)[/tex] are [tex]\((6, -13)\)[/tex].
So the coordinates of [tex]\(B'\)[/tex] are:
[tex]\[
\boxed{(6, -13)}
\][/tex]
