Circle Dilation Animation

In grade IX transformation geometry, students learn reflection, rotation, translation, and dilation. This article explains how to create a circle dilation animation in GeoGebra.

Dilation is a transformation that changes the size of a figure, either enlarging or reducing it, without changing its shape.

Steps to Create a Circle Dilation Animation in GeoGebra

1. Open GeoGebra

Open the GeoGebra application on your computer or device.

2. Create Points A and B

Create point $A$ at coordinates $(3,2)$ and point $B$ at coordinates $(0,0)$.

3. Create a Slider

Click the Slider tool, then click anywhere on the workspace. Fill in the slider form as needed, similar to the example below.

4. Create the First Circle

Enter the following command to display a circle centered at point $A$:

c = Circle[A,2]

The result will look like this.

5. Create Point C and the Second Circle

Create another point, $C(3,-2)$, then create a circle centered at point $C$ with the command:

e = Circle[C,2]

6. Create the Dilated Points

Create the dilation images of points $A$ and $C$ using the following commands:

A' = Dilate[A,a,B]
C' = Dilate[C,a,B]

7. Create the Dilated Circles

Enter the following commands to display the dilated circles:

d = Dilate[Circle[A,2],a,B]
f = Dilate[Circle[C,2],a,B]

The result will look like this.

8. Enable Trace

To make the movement easier to observe, right-click each circle, choose Object Properties, then enable Show Trace in the Basic section.

9. Change the Color and Move the Slider

Change the color of one circle so the two circles are easier to distinguish. Then move the slider to observe the enlargement and reduction process.

10. Tidy the Appearance

Tidy the circles, slider, and graph display. Below is an example of the finished animation. Click the play icon in the lower-left corner or move the slider manually.

That concludes this guide to creating a circle dilation animation in GeoGebra. If you have suggestions or corrections, please leave them in the comments.