
1. Open GeoGebra and select Algebra & Graphics from the Perspectives menu. 

2. To show labels of new constructed points only, click the Options menu, click Labeling, then click New Points Only. 

3. We create a circle with center (0,0) and radius 1. To construct point A, the center of the circle, select the Intersect Two Objects tool, click the xaxis, then click the yaxis. 

4. To construct the circle with center A and radius 1, type circle[A,1] and press the ENTER key on your keyboard. 

5. Next we construct a point on the circle and color it red. To construct point B on the circle, select the New Point tool and click the circumference of the circle. Be sure that point B is on the circle. If not, delete it and repeat the construction. 

6. We now reflect point B about the yaxis and xaxis. To do this, select the Reflect Object About Line tool, select point B and then click the xaxis. This will produce B’. Your drawing should look like Figure 1.
Figure 1


7. Now we reflect B about the yaxis. To do this, with the Reflect Object About Line tool still active, click point B and click the yaxis. Notice that the label of the B’ changed to B’_{1} and the newly produced point became B’.
Figure 2 

8. Now, reflect B’ about the yaxis to construct the fourth vertex of the rectangle. 

9. Now, we change the color of point B to red or any color not blue. 

10. We now rename the bluecolored points. Right click each point, select Rename from the context menu and change the names of the blue points to C, D, E as shown in Figure 3. 

12. Next, we use the Polygon tool to construct rectangle BCDE. Select the Polygon tool, and click in the following order: B, C, D, E and B to close the polygon. Note that the rectangle’s name is poly1 (see Algebra view). 

13. Next, we will construct circle with radius poly1. The value of poly1 in the Algebra view is the area of the rectangle. To do this, type circle[A,poly1] and press the ENTER key on your keyboard. 

14. Select the Ray through Two Points tool, select point A and select point B to construct ray AB. 

15. Next, using the Intersect Two Objects tool, intersect Ray AB and the new constructed circle This will produce point F. This means that the length of AF is equal to the area of the rectangle.
Figure 3


16. Next, we hide the ray and the circle containing point F. To do this, right click each object and click Show Object from the context menu. 

17. Connect AF using the Segment Between Two Points tool. 

18. We now trace point F. To do this, right click point F and select Trace On from the context menu. Now, move point B along the circle. The trace should look like Figure 3.
Figure 5 

19. Now, to create a solid curve tracing the Select the Locus tool, select point B and select point F. Now, your drawing should look like Figure 5. 

20. Now, use the Move tool and move the drawing pad. 

21. Hide the names of the points by rightclicking each point and selecting Show label.
Figure 6 