(Originais Teachy 2023) - Question Hard of Mathematics

To calculate the area of a triangle in the Cartesian plane, it is common to use the concept of determinants and the area formula A = 0.5 * |det(M)|, where M is the matrix formed by the coordinates of the triangle's vertices. Consider the triangle with vertices A(1,0), B(2,3), and C(4,1). Determine the area of this triangle using the concept of determinants and Sarrus' rule for calculating determinants of a 3x3 matrix. Show all the calculation steps and explain the meaning of the negative sign that may appear in the determinant in relation to the orientation of the triangle in the Cartesian plane.