Point in a Square

A point is located in a square. Distances are drawn to either the sides of the square or to its vertices. This applet provides an environment to explore under what circumstances the four distances can form a quadrilateral, and if they can, what can be said about the quadrilateral formed. Move the yellow point in the left panel to set the four distances. In the right hand panel choose one of two ways to link the four distances to one another to form a quadrilateral – either BLUE - BLUE - GREEN - GREEN [BBGG] or BLUE - GREEN - BLUE - GREEN [BGBG] You can drag the white and black dots to form quadrilaterals. [N.B. The yellow dot in the right hand panel allows you to translate the linkage without deforming it.] What can you say about the kinds of quadrilaterals that you can form with each linkage of the distances [i.e., to the sides or to the vertices] ? Are there quadrilaterals that can be formed with one linkage but not the other? Are there quadrilaterals that cannot be formed at all by either linkage ? What questions could/would you put to your students based on this applet?