To translate a point \( A \) with coordinates \( (x, y) \) by 5 units left and 3 units up, you would subtract 5 from the x-coordinate and add 3 to the y-coordinate.
The translation can be represented as:
\[ (x, y) \rightarrow (x - 5, y + 3) \]
Now let's examine the options:
- Option #1: \( (x, y) \rightarrow (x - 5, y + 3) \) — This is correct, as it matches the translation specified.
- Option #2: \( (x, y) \rightarrow (5x, 3y) \) — This is incorrect, as it involves scaling rather than translating.
- Option #3: \( (x, y) \rightarrow (x + 3, y - 5) \) — This is incorrect, as it moves the point in the opposite direction.
Based on this analysis, the correct option for translating \( A \) 5 units left and 3 units up is Option #1: (x, y) → (x - 5, y + 3).
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