How to Rotate a Point
You can rotate a point by an angle in several different ways. You can specify the angle of rotation during the rotate process, or you can reference a previously measured angle.
To specify the angle of rotation during the rotate process, choose the Rotate around Point tool. Click on the point A (the point that we are going to rotate), then on point B (the center of rotation). A dialog box will appear where you can enter the angle of rotation in degrees. You can also specify whether the rotation is to be counterclockwise (the default) or clockwise.
To rotate an angle by a previously measured angle (an angle from somewhere else on your drawing that you would like to duplicate), you must first measure that angle.
Choose the Angle tool from the toolbar, then choose points C, A and B (in that order). This measures angle CAB, and the angle measure appears in the Algebra window on the left.
Now choose the Rotate around Point tool. Click on Point D (the point we are going to rotate), and then the point marked Center (the center of rotation). This time, when the dialog box pops up, delete the default value of 45 degrees, and click on the little alpha symbol at the right side of the box. This brings up all the angle variables that Geogebra uses. Since the measured angle is alpha, choose the alpha symbol from the box, then click on "OK." This will rotate point D around the center by whatever the measured angle was. The advantage to this method is that if the original angle changes, D' will change, too. Check this by moving points A, B and/or C to change the measure of the angle, and notice how D' changes.