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Dilate Geometric Objects in Cabri Jr. on the TI-84 Plus

You can dilate geometric objects in the Cabri Jr. geometry application for the TI-84 Plus calculator. The Dilation tool in the in the F4 Transformation menu 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 (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 picture shows that the already constructed triangle is to be dilated with respect to a point outside the triangle.

    image0.jpg
  2. Use the Alpha-Num tool in the F5 Appearance menu to place the value of the dilation factor k anywhere on the screen.

    To do this, press [GRAPH] to access the Appearance menu. Use

    image1.png

    to move the cursor to the Alpha-Num option and press [ENTER] to select that option. Move the cursor to an out-of-the-way location on the screen and press [ENTER]. Press [ALPHA] and use the keypad to enter the value of the dilation factor k and press [ENTER]. This is illustrated in the first picture, where the dilation factor is placed in the upper-right corner of the screen.

  3. Press [TRACE] to access the F4 Transformation menu. Use

    image2.png

    to move the cursor to the Dilation option and press [ENTER] to select that option. Then use the arrow keys to move the cursor to the object you want to dilate and press [ENTER].

    Cabri Jr. can dilate only one object at a time. The object to be dilated blinks when the cursor is placed on it. When selecting a triangle or quadrilateral, all sides of the object must be blinking to select the whole object instead of just one side of the object. To do this, place the cursor inside the object and move it slightly until all sides are blinking.

  4. Use the arrow keys to move the cursor to the dilation point and press [ENTER]. Then use the arrow keys to move the cursor to the dilation factor you entered in Step 2 and press [ENTER].

    The original object and the dilation of the object appear on the screen.

  5. Repeat Steps 3 and 4 to dilate more objects. When you are finished dilating objects, press [CLEAR] or select another menu item.

After dilating objects, if you move the center of dilation, the dilated object moves to the location determined by the new center.

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