To understand how to rewrite the translation rule [tex]\( T_{-3,5}(x, y) \)[/tex], let’s break down the components of what this translation means.
The given translation rule is [tex]\( T_{-3,5}(x, y) \)[/tex]. This notation indicates that every point [tex]\((x, y)\)[/tex] on the coordinate plane is being translated as follows:
- The x-coordinate of the point is shifted by [tex]\(-3\)[/tex].
- The y-coordinate of the point is shifted by [tex]\(+5\)[/tex].
Let’s translate a generic point [tex]\((x, y)\)[/tex] with this rule:
- The new x-coordinate will be [tex]\( x - 3 \)[/tex]:
[tex]\[
\text{New x-coordinate} = x - 3
\][/tex]
- The new y-coordinate will be [tex]\( y + 5 \)[/tex]:
[tex]\[
\text{New y-coordinate} = y + 5
\][/tex]
Combining these, we find that the translation rule transforms the point [tex]\((x, y)\)[/tex] to:
[tex]\[
(x, y) \rightarrow (x-3, y+5)
\][/tex]
Now we shall review the given options to see which matches this resultant transformation:
1. [tex]\((x, y) \rightarrow(x-3, y+5)\)[/tex]
2. [tex]\((x, y) \rightarrow(x-3, y-5)\)[/tex]
3. [tex]\((x, y) \rightarrow(x+3, y-5)\)[/tex]
4. [tex]\((x, y) \rightarrow(x+3, y+5)\)[/tex]
From our transformation [tex]\( (x, y) \rightarrow(x-3, y+5) \)[/tex], the correct option is:
[tex]\[
(x, y) \rightarrow (x-3, y+5)
\][/tex]
Therefore, the correct option is the first one:
[tex]\[
\boxed{(x, y) \rightarrow (x-3, y+5)}
\][/tex]
