Area of Triangle in Coordinate Geometry

In the Cartesian coordinate plane, consider the triangle formed by the points A(2, 3), B(5, -1), and C(-1, 4). You need to determine the area of this triangle using the formula for the area based on the coordinates of its vertices. The formula for the area of a triangle with vertices at coordinates $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ is given by:

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

Using this formula, compute the area of triangle ABC.