Excuse me, do you know rotations?

Geometry Level 3

There are points \( A(1, 1) \), \( B(5, 9) \) and \( C(2, 3) \). Also, there is an ambigious point \( R \) with unknown coordinates. A rotation is performed, with \( R \) as centre of the rotation. It is known that \( A' \), \( B' \) and \( C' \) are points \( A \), \( B \) and \( C \), respectively, after rotation. It is also known that \( A'(3, -5) \) and \( B'(11, -9) \). Calculate the are of triangle \( ABC' \)

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