To determine which rigid transformation would map triangle \( \Delta AQR \) to triangle \( \Delta AKP \), we need to analyze the points and their relationships in both triangles.
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Rotation about point A: This transformation would change the position of points \( Q \) and \( R \) around point \( A \), which could potentially match them to \( K \) and \( P \).
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Reflection across the line containing AR: A reflection across that line would not necessarily ensure that \( Q \) maps to \( K \) and \( R \) maps to \( P \).
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Reflection across the line containing AQ: Similar to the previous point, a reflection across the line containing \( AQ \) would not ensure that the points correlate as needed.
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Rotation about point R: This would change the position of points around \( R \), which may not necessarily correspond to the desired mapping of \( Q \) to \( K \) and \( R \) to \( P \).
Given that the problem states that triangle \( AQR \) is rotated up and to the right to form triangle \( AKP \), the most fitting transformation in this context would be:
a rotation about point A
Hence, the correct option is to rotate \( \Delta AQR \) about point \( A \) to map it onto \( \Delta AKP \).