The Dilation tool in the in the TRFM menu on the TI-84 Plus is used to increase or decrease the size of an object by a factor of k. When 0 < k < 1, the object decreases in size, and when k > 1, it increases in size.

For example, if k = 0.5, the dilated object is half its original size, and if k = 2, the dilated object doubles in size. Guess what it does when k = 1? That’s right: The object doesn’t change at all.

The dilation of an object also takes place with respect to a fixed point appropriately called the dilation point. If that point is at the center of the object, such as the center of a circle, the object increases or decreases in size and the center of the object remains fixed.

But when the dilation point is not in the center of the object, not only does the object increase or decrease in size, but it also moves away from the dilation point when k > 1 or closer when 0 < k < 1. The distance that the dilated object moves is determined by k. For example, if k = 2, the dilated object doubles in size and is twice as far away for the dilation point.

To dilate an already constructed geometric object, follow these steps:

1. Construct the dilation point.

The dilation point can be one of the points on the already constructed object. The first image shows that the already constructed pentagon is to be dilated with respect to a point outside the pentagon.

2. Press [GRAPH][TRACE][4] to select the Dilation tool from the TRFM menu.

3. Use the arrow keys to move the cursor to the object you want to dilate and press [ENTER].

GeoMaster can dilate only one object at a time. The object to be dilated appears as a dashed figure.

4. Use the arrow keys to move the cursor to the dilation point and press [ENTER].

5. Use the keypad to enter the dilation factor k.

As you begin to enter the dilation factor,

appears in the lower-left corner of the screen, and the calculator places your entry after this symbol. The second image illustrates that the pentagon is about to be reduced to half its size and moved halfway closer to the dilation point.

Instead of entering the dilation factor, you can repeatedly press [+] and/or [–] to dilate the object about the dilation point. Each time you press [+], the object is increased in size by a factor of 1.1; [–] decreased its size by a factor of 0.9.

6. Press [ENTER].

The original placement of the object vanishes and the dilation of the object appears on the screen.

The dilation tool remains active until you deactivate it. So if you want to dilate another object, repeat Steps 3 through 6. When you are finished using the tool, deactivate it by pressing [CLEAR] or by selecting another menu item.