



 This page focuses on the use of transformation tools. Viewlets are provided to demonstrate the constructions in the first file. Some pages of the first file are converted into Java applets and can be opened directly in the web browser.






 Transformation and Symmetry





 The 'Transform' menu provides tools for performing and exploring transformation (translation, reflection, rotation and dilation) of 2D figures. Sometimes these tools can be useful means, and even shortcuts, for constructing geometric objects.






 translation by a marked vector: specify a vector by selecting its endpoints on screen or entering numerical values for its components






 This JavaSketchpad file shows a triangle ABC and its image A'B'C' under a translation defined by the vector A > A'. Drag A' to change the translation.






 reflection by a marked mirror (line or line segment)






 This JavaSketchpad file shows a triangle ABC and its reflected image about the line through P, Q. Move P or Q to change the mirror.






 rotation by a marked center and angle: specify an angle by entering its size (fixed angle) or selecting the 3 vertices that define an angle (the angle could be then controlled through the mouse)






 rotation by a hidden marked angle






 This JavaSketchpad shows a triangle ABC and its image after rotation by the angle AcenterA'. Move A' to change the angle of rotation.






 dilation by a marked center and ratio: the ratio can be specified by entering numerical values or selecting 3 points on a straight line (e.g. to mark the ratio AB to AC, select the points in the order A, C, B.)






 This JavaSketchpad shows a triangle ABC and its dilated image A'B'C'. A' lies on the line through the center and A. Adjust the position of A' to change the dilation factor. Negative factor is allowed.






 another way to demonstrate translation






 drag Z on the line XY to change the dilation factor






 construct a polygon with 3 axes of symmetry






 polygon with 1 axis of symmetry






 polygon with 2 axes of symmetry






 polygon with 3 axes of symmetry






 construct a polygon with rotational symmetry of order 3






 rotate the image of a figure to check its symmetry






 rotational symmetry of order 2






 rotational symmetry of order 3






 reflection of a point about a line in the coordinate plane; compare coordinate of the original point and the image






 drawing and checking reflection of a polygon about a line, working on a dotted square grid






