In the coordinate plane, a triangle has vertices at points A(2, 3), B(4, 7), and C(6, 3). The triangle is reflected across the line $y = x$ to create triangle A'B'C'. What is the area of triangle A'B'C'?

Recall that the area of a triangle given its vertices at $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ can be calculated using the formula:

$$ ext{Area} = rac{1}{2} imes |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| $$