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Dynamic visualization of the relative position of straight lines on the plane using Mathematica

This paper presents a proposal based in the graphical capabilities as a programming language of the system Mathematica in order to improve the mathematical knowledge and the visualization skills of first-year engineering students. By means of the dynamic contents of the command Manipulate this initiative tries to improve the comprehension of some algebraic contents related with the Euclidean geometry, more specifically, the relative position of two or three straight lines on the plane. To achieve this objective, it has been developed a specific procedure divided into two parts. The first of them allows students to fix the parameters of a straight line on the plane and to modify dynamically (by using a cursor) the parameters of a second straight line between some pre-specified values, which can also be modified by the user. Both lines are represented simultaneously on a window, which offers immediate information about the relative position, and which also gives the value of the distance between the lines if they are parallel, or the coordinates of their common point if they cross. In a second step, the procedure has been extended to fix two straight lines and to visualize and analyze dynamically the behavior of a third line and its relative position with respect to the previous two lines. This proposal aims to help teachers of mathematics to make their students to have a better understanding of these algebraic concepts: it allows visualizing the consequences of variations in any of the parameters of a straight line, and obtains dynamically and immediately the relative positions of two or more straight lines.