



 The following examples describe some basic geometric transformations in Geogebra. We show the steps for reflecting or rotating an inserted picture. The same procedures can be applied to other geometric objects such as points or polygons.






 Choose the mode "Insert image", then click a point to start the insertion. The point is used to define the lower left corner of the picture. When a dialog window (see below) is opened, navigate through your folders to find the image file prepared and click "Open".





 Step 2: Reflect the picture in a line






 Add a line in your drawing pad. Choose the mode "Mirror object at line". Click the picture (the object to be reflected), then the line (as the mirror line). An image will be created.






 When the image is formed, try to change the position of the original picture (drag A) or the points that define the mirror line (drag B or C) to explore the effect on the image.





 Rotation of a figure, with a fixed angle





 Step 1: Insert a picture, the same step in the example above





 Step 2: Rotate the picture about a point by 90 degrees






 We'll rotate the picture about point B. After the choosing the mode for rotation, click the picture (the object to be rotated), then the point B as center of rotation. A dialog window will appear (see below) to prompt for the angle of rotation. Enter the size of the angle (e.g. 90 degrees) and choose the direction.






 In this example, we enter a fixed angle. Drag A or B afterwards to find out the effect on the image.





 Rotation of a figure, by a variable angle





 Step 1: Insert a picture, the same step in the example above






 Make a circle, centered at B (which is also the center of rotation) and through A. Add a point C on this circle. C should be freely movable on the circle and becomes an image of A under a rotation about B.






 Make an angle ABC, by clicking the points A, B and then C. This angle is named alpha and it can be used to define the subsequent angle of rotation.





 Step 3: Rotate the picture by the marked angle





 Repeat step 2 in the previous example. When the dialog window appears, enter the angle alpha (or name of any angle you have defined). The Greek letters can be chosen from the pull down menu provided on the right of the dialog window. As the picture is rotated by the angle alpha, when you drag C, the image will follow. Hide the circle afterwards.






 In this example, 2 more points are added to control the shape of the original picture. Right click on the picture to open its dialog for editing properties. Choose a point for "Corner" 2 and/or 4 from the pull down menu.





 The following examples show two regular pentagons constructed by using rotating points with given angles. Study the construction protocols to find how they can be done.






 Regular pentagon on a given side






 Regular pentagon with a given center






