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 $$ABC'$$

×