Geometry Explorer Help

The Tool Panel:

Transform Sub-Panel:

(Help Main Page)

transform panel

Transformations are carried out in a two-stage process. First, you must specify the geometric information that defines a transformation. Then, you must select the objects to be transformed and click on the appropriate transform button.

One non-obvious feature about the transformation panel is the fact that the "Mark", "Custom", and "Base"  labels are actually pull-down menus. These are used to set transformation information and to define compound transformations.


Specification of Transformation Parameters:
translate To Translate a figure: You must specify a vector. This can be done by either selecting two points on the canvas and using the "Vector" item in the "Mark" menu, or by selecting the "Translation" item in the "Custom" menu. When you select the "Translation" item, a box will appear on the screen, and you can then specify the particular direction and magnitude you desire (example).  Additionally, a translation vector can be specified by selecting two measured quantities and choosing "Vector." In this case a box will appear asking if the two measurements are to be interpreted as rectangular or polar translation coordinates.

rotate To Rotate a figure: You must specify an angle and a center. You can select the angle by selecting any three points on the canvas and then choosing the "Angle" item in the "Mark" menu, or you can specifically define it by choosing the "Rotation" item in the "Custom" menu and then entering the desired angle (in degrees) into the box.  A third way to define an angle is by selecting a measurement and then choosing "Angle."  The center is determined by selecting a point and choosing the "Center" item in the "Mark" menu.

dilate To Dilate a figure: You must specify a ratio and a center. You can define the ratio by selecting two segments in the canvas and then choosing the "Ratio" item in the "Mark" menu (the length of the first segment that was selected will be the numerator of the ratio, and the length of the second segment will be the denominator of the ratio), or you can choose the "Dilation" item in the "Custom" menu to specify the ratio that you would like to use.  A third way to define a ratio is by selecting a measurement and then choosing "Ratio."  You define the center point of the dilation by selecting a point on the canvas and then choosing "Center" in the "Mark" menu.

reflect To Reflect a figure: You must specify a mirror. You can do this by selecting a segment, a line, or a ray upon the canvas and then choosing the "Mirror" item in the "Mark" menu.


Activating the transformation on an object(s): When the appropriate information has been specified, you will need to select an object or group of objects on the canvas before the particular transformation button will become enabled. Once the selection has been made, the button will get darker in appearance to signify that the transformation can be applied. When you click on the particular button, the transformation is automatically applied. Here is what each of the transformations actually does once you click on it:

Translation: The object is simply moved along the specified vector to a different location. This is somewhat like dragging the object, but with more control over where it goes.

Rotation: The object is rotated about a specified center to a specified angle. It is as though the object is attached to the center with strings and is swung around to whatever angle you choose.

Dilation: The object is shrunk or expanded (depending upon whether the ratio is smaller than or bigger than 1.0) with respect to the center point. For example, if the ratio specified is 1/2, when you click on the dilation button, the selected object will move halfway to the center point and will shrink to half its size. Pressing the button again will re-apply the transformation, this time using the shrunken image as the selected object.

Reflection: The object is reflected about a mirror. This transformation acts as the name implies; once you select a segment, ray, or line as a mirror, clicking this button results in an exact reflection of the selected object on the other side of the mirror.


Controlling Transformations using the "Base" Menu: Under the Base menu there are three options. These can be used to specify how a transformation will act on the base elements that it transforms.


Other Custom Transformation Capabilities:

Moebius Transformations: Under the "Custom" menu in the Transform Panel there is a menu option titled "Moebius...." This option can be used to define special transformations in Hyperbolic Geometry (example).