Area of Triangle in Coordinate Geometry

Consider a triangle formed by the points A(1, 2), B(4, 6), and C(7, 1) in the Cartesian plane. Determine the area of triangle ABC using the coordinate geometry formula.

The formula for the area of a triangle when the vertices are given by coordinates \\( (x_1, y_1), (x_2, y_2), (x_3, y_3) \\) is:

$$ Area = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| $$

Use this formula to calculate the area of triangle ABC.