Let's break down the instructions that John has given:
1. Travel 5 blocks west:
- West corresponds to moving left on the [tex]\(x\)[/tex]-axis. Therefore, traveling 5 blocks west means decreasing the [tex]\(x\)[/tex]-coordinate by 5 units. If the original coordinates are [tex]\((x, y)\)[/tex], then the new [tex]\(x\)[/tex]-coordinate would be [tex]\(x - 5\)[/tex].
2. Travel 3 blocks north:
- North corresponds to moving up on the [tex]\(y\)[/tex]-axis. Therefore, traveling 3 blocks north means increasing the [tex]\(y\)[/tex]-coordinate by 3 units. If the original coordinates are [tex]\((x, y)\)[/tex], then the new [tex]\(y\)[/tex]-coordinate would be [tex]\(y + 3\)[/tex].
Combining these two steps, the translation rule would be:
[tex]\[
(x, y) \rightarrow (x - 5, y + 3)
\][/tex]
We can now compare this to the given options:
1. [tex]\( (x, y) \rightarrow (x+5, y-3) \)[/tex]
2. [tex]\( (x, y) \rightarrow (x-5, y+3) \)[/tex]
3. [tex]\( (x, y) \rightarrow (x+3, y-5) \)[/tex]
4. [tex]\( (x, y) \rightarrow (x-3, y+5) \)[/tex]
Clearly, the correct translation rule, which corresponds to John's instructions, is:
[tex]\[
\boxed{(x, y) \rightarrow (x-5, y+3)}
\][/tex]
Thus, the correct option is the second one, which translates to:
[tex]\[
(x-5, y+3)
\][/tex]
Therefore, the answer is:
[tex]\[
\boxed{2}
\][/tex]
