Consider a triangle represented by $A(0, 0), B(1, 1), C(5, 2)$. The triangle is rotated by $45$ degrees about a point $P(-1, -1)$. The co ordinates of the new triangle obtained after rotation shall be ________.
- $A'(-1, \sqrt{2}-1), B'(-1, 2\sqrt{2}-1), C'\left(\frac{3}{2}\sqrt{2}-1, \frac{9}{2}\sqrt{2}-1\right)$
- $A'(\sqrt{2}-1, -1), B'(2\sqrt{2}-1, -1), C'\left(\frac{3}{2}\sqrt{2}-1, \frac{9}{2}\sqrt{2}-1\right)$
- $A'(-1, \sqrt{2}-1), B'(2\sqrt{2}-1, -1), C'\left(\frac{3}{2}\sqrt{2}-1, \frac{9}{2}\sqrt{2}-1\right)$
- $A'(-1, \sqrt{2}-1), B'(2\sqrt{2}-1, -1), C'\left(\frac{9}{2}\sqrt{2}-1, \frac{3}{2}\sqrt{2}-1\right)$
