Help: Isometry Transformations
Using this manipulative you may view the effect of applying reflection, translation, and rotation transformations. You may:
Add blocks to the workspace
- Click on a block in the shape toolbar to the right of the workspace.
The block will be added to the workspace.
You may add more than one block.
- Move blocks in the workspace by clicking and dragging them.
- Rotate a block by clicking on one of its corners, holding the mouse button down, and moving the mouse in a circular motion.
Apply a transformation
To apply a transformation to the objects in the workspace, click on one of the following buttons to the left of the workspace.
 |
Reflection |
 |
Translation |
 |
Rotation |
The button you clicked on will be depressed and an item representing the transformation will be shown in the workspace:
- Reflection reflection line
- Translation translation vector
- Rotation rotation angle
The selected transformation will be applied to all blocks in the workspace.
You may dynamically view the effect of modifying the transformation by following the instructions below.
Move or rotate a reflection line
- Move a reflection line by clicking and dragging the solid black point on it.
- Rotate a reflection line by clicking and dragging in a circular motion any point on it except the solid black point.
Modify a translation vector
- Move a translation vector by clicking and dragging the base (non-arrow end).
- Rotate or change the length of a translation vector by clicking and dragging the tip (arrow end).
Modify a rotation transformation
- Move the origin of a rotation transformation by clicking and dragging the center of the displayed angle.
- Change the start angle of a rotation transformation by clicking and dragging the tip of the line at which the angle begins.
- Change angle of a rotation transformation by clicking and dragging the tip of the line at which the angle ends.