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John left a scavenger hunt for his friends! He advised his friends to travel 5 blocks west and 3 blocks north. Which translation rule below describes John's instructions?

[tex]\[
\begin{array}{l}
(x, y) \rightarrow(x+5, y-3) \\
(x, y) \rightarrow(x-5, y+3) \\
(x, y) \rightarrow(x+3, y-5) \\
(x, y) \rightarrow(x-3, y+5)
\end{array}
\][/tex]



Answer :

GinnyAnswer
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]

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