Transformations - Dilation
With this virtual manipulative you can create objects with pattern block pieces and explore Dilations of the plane.
Change the scale (size) of the dilation by moving the slider below the workspace.
Click and drag the dot that marks the center of dilation. Original objects continue to be dynamically dilated. The first original is visually connected to its image by the line from the center. When another object is placed on the workspace, its dilated image appears also, but be careful; the image of a new object may not be visible if the dilation takes it off-screen. You can move the new original or the dilation slider to make the image show in the workspace.
Place and move objects in workspace
Click on any desired shape button. Each piece enters separately. When the first object is placed on the workspace, a line from the center of dilation (dot) shows that the dilation moves the original toward or away from the center. When more objects are entered, they are dilated by the same amount (scale factor) as the first, and the image is on the line from the center through the original, but only one line is shown (through the first object). You can select, slide, or rotate each original individually, and its dilated image does the same thing. You can also change the color of any selected original piece (choose from the color palette) and the transformed images change color at the same time.
To delete, select an original object or group by clicking on it (black dots show what is selected), and then click the button. When the first object (the one showing the translation vector) is deleted, the translation arrow moves to another object. The button removes everything from the workspace.
Click and hold down the mouse button to "lasso" (draw a rectangle around) two or more original objects, then release. The objects thus grouped now move and rotate together.
To ungroup, hold down the Shift key in your keyboard while clicking and dragging a rectangle around the group to separate. When you release the mouse button, the group will be separated and you may now select each object individually.
The lattice points in the background of the workspace are for convenience in visualizing the effects of a dilation transformation. To add (or remove) coordinate axes (horizontal and vertical), click in the box at the corner of the workspace. The axes are not active, but you can place the center of dilation at a particular point to help see what a dilation does to coordinates.