# Developing the Concept of a Determinant using DGS

- Author:
- 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.