To determine the correct transformation that translates the vertex from \((-5, 5)\) to \((0, 2)\), we can analyze the movements along the x-axis and y-axis.
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X-axis movement: From \(-5\) to \(0\), you need to shift to the right by \(5\) units (since \(0 - (-5) = 5\)).
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Y-axis movement: From \(5\) to \(2\), you need to shift down by \(3\) units (since \(2 - 5 = -3\)).
Therefore, the transformation that translates the vertex from \((-5, 5)\) to \((0, 2)\) is:
- Shift right 5 units and down 3 units.
None of the provided options exactly match this description, but the closest corresponding choice is:
Shift right 5 units and down 3 units.