Triangle \( ABC \) has vertices at \( A(1, 3) \), \( B(4, 7) \), and \( C(6, 2) \). The triangle is reflected over the line \( y = x \) to form triangle \( A'B'C' \). Calculate the area of triangle \( A'B'C' \). Let's think step by step and output the final answer within \boxed{}.
user