To translate \(\Delta ABC\) 5 units left and 3 units up, you want to adjust the x-coordinate and y-coordinate of each point as follows:
- Moving 5 units left means you subtract 5 from the x-coordinate.
- Moving 3 units up means you add 3 to the y-coordinate.
Based on this, the correct transformation would be:
\[ (x, y) \rightarrow (x - 5, y + 3) \]
Now let's evaluate the options:
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Option #1: \((x,y) \rightarrow (x - 5, y + 3)\) is correct.
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Option #2: \((x,y) \rightarrow (5x, 3y)\) does not represent a translation but rather a scaling transformation, which is not what we want.
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Option #3: \((x,y) \rightarrow (x + 3, y - 5)\) would move a point 3 units to the right (not left) and 5 units down (not up), which is also not correct.
Therefore, the correct answer is Option #1: \((x,y) \rightarrow (x - 5, y + 3)\).