Developing the Concept of a Determinant using DGS

Ana DT_1
Set the vertices of the parallelogram to obtain the following figures: Square ABCD with side 1 Square ABCD with side a Rectangle ABCD with sides a and b Triangle ABD Write the coordinates of the vertex B and D, the matrix and the determinant representing the corresponding area. Provide proves.
Task1. Provide a visualization of any determinant and explain the relation between the determinant and the area of the geometric figure you have presented. Write a property in general terms for this task. Task 2. Write the area of a trapezoid ABCD with vertices A(0,0), B(6,2), C(4,4) and D(1,3) using determinants. Task 3. Find the area of the triangle such that none of its vertices coincide the origin of the Descartes coordinate system.