To understand the translation rule [tex]\( T_{-8,4}(x, y) \)[/tex], let's break it down step-by-step.
1. Translation Rules: Translating a point [tex]\((x, y)\)[/tex] by [tex]\((a, b)\)[/tex] means shifting the point by [tex]\(a\)[/tex] units horizontally and [tex]\(b\)[/tex] units vertically. The general translation rule is written as:
[tex]\[
(x, y) \rightarrow (x + a, y + b)
\][/tex]
2. Given Translation: In the problem, we are given the translation rule [tex]\( T_{-8, 4}(x, y) \)[/tex]. This can be interpreted as:
- Shift the point [tex]\((x, y)\)[/tex] by [tex]\(-8\)[/tex] units horizontally.
- Shift the point [tex]\((x, y)\)[/tex] by [tex]\(4\)[/tex] units vertically.
3. Applying the Translation: Using the general form of the translation rule:
[tex]\[
(x, y) \rightarrow (x + (-8), y + 4)
\][/tex]
Simplifying this, we get:
[tex]\[
(x, y) \rightarrow (x - 8, y + 4)
\][/tex]
4. Another Way to Write the Rule: Therefore, the translation rule [tex]\( T_{-8, 4}(x, y) \)[/tex] can be written as:
[tex]\[
(x, y) \rightarrow (x - 8, y + 4)
\][/tex]
5. Identifying the Correct Option: Among the given options, the one that matches this translation rule is:
[tex]\[
(x, y) \rightarrow (x - 8, y + 4)
\][/tex]
Therefore, the correct way to write this translation rule is:
[tex]\[
(x, y) \rightarrow (x - 8, y + 4)
\][/tex]
This corresponds to the third option. So, the correct answer is:
[tex]\[
(x, y) \rightarrow (x - 8, y + 4)
\][/tex]
