To understand the transformation given by the mapping \( (x, y) \to (y + 5, -x) \), we can break it down into two components: the transformation of the coordinates and then the translation.
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Transformation of coordinates:
- The \(x\)-coordinate changes from \(x\) to \(-x\), which indicates a reflection across the \(y\)-axis.
- The \(y\)-coordinate changes from \(y\) to \(y + 5\), which indicates a vertical translation upward by 5 units.
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Analyzing Rotation:
- To determine if a 90-degree rotation is involved, we can observe that a 90-degree counterclockwise rotation around the origin transforms \((x, y)\) to \((-y, x)\), and a 90-degree clockwise rotation transforms \((x, y)\) to \((y, -x)\).
- The mapping given here, \((x, y) \to (y + 5, -x)\), does not conform exactly to the standard forms of the rotations mentioned. However, we note that it reflects in some way since it includes the \(-x\) transformation.
In conclusion, based on the components analyzed:
- The transformation involves a vertical translation up by 5 units.
- It also includes a reflection.
Neither of the options A or B (which suggest pure rotations) accurately captures the combined transformations given in the function. However, since the rotation aspect is more commonly focused upon, it is clearer that the translation is vertical, which means the options could be misleading.
If we strictly adhere to the options given:
- Option A describes a 90-degree counterclockwise rotation which does not apply here, nor does it capture the upward translation correctly.
- Option B describes a 90-degree clockwise rotation, which is also misaligned due to the translation.
Therefore, neither option A nor B is correct for the transformation described. The transformation can be best described as involving reflection (horizontal flipping) and translation (vertical upward shift) but does not fit strictly into the rotation categories mentioned.
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