Triangle Area on the Coordinate Plane

In a coordinate plane, the points A(2, 3), B(6, 11), and C(x, y) form the vertices of a triangle. The area of triangle ABC is given by the formula:

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

where the coordinates of the points are $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$. If the area of triangle ABC is 16 square units, determine the value of $$x$$ when point C is located on the line segment between A and B.