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

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



Answer :

GinnyAnswer
To determine the translation rule that describes Johr's instructions, let's go through the step-by-step process he advised.

### Johr's Instructions
1. Travel 5 blocks west:
- Moving west means decreasing the x-coordinate. For each block traveled west, the x-coordinate decreases by 1.
- Therefore, traveling 5 blocks west decreases the x-coordinate by 5.
- Mathematically, this is represented as [tex]\( x \rightarrow x - 5 \)[/tex].

2. Travel 3 blocks north:
- Moving north means increasing the y-coordinate. For each block traveled north, the y-coordinate increases by 1.
- Therefore, traveling 3 blocks north increases the y-coordinate by 3.
- Mathematically, this is represented as [tex]\( y \rightarrow y + 3 \)[/tex].

### Combining Both Movements
Combining both of these movements into a translation rule for coordinates [tex]\((x, y)\)[/tex], we get:
[tex]\[ (x, y) \rightarrow (x - 5, y + 3) \][/tex]

### Selecting the Correct Option
Now, let's match this derived translation rule to the options given:

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

Clearly, the translation rule [tex]\((x - 5, y + 3)\)[/tex] matches option (C).

### Conclusion
The translation rule that describes Johr's instructions is:

[tex]\[ (x, y) \rightarrow (x - 5, y + 3) \][/tex]

Therefore, the correct option is [tex]\(\boxed{C}\)[/tex].

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