GeoGebra Classroom

# Dilation Demonstration Version 1

## I was trying to create something similar to the Nspire programs, but free. Also, I really like check boxes.

The first thing I'd like you to do is to play around with the stuff in the applet. Drag a single point around, or an entire triangle, and watch what happens to the rest of the objects in the picture. Alter the scalar on the slider and watch what happens to the figures then. As you're playing and watching, see if you can't start to figure out what the rules of this game are.

You may have noticed that you're not allowed to drag any of the purple points. Why is that?

Why didn't I let the scalar be a negative number? What might have happened if I did?

Make a conjecture about the relationship of the perimeters of triangle ABC and its image, triangle A'B'C'. Click the check box to reveal the respective perimeters. Were you right? If not, what was your error? Why does this relationship make sense?

Make a conjecture about the relationship of the areas of the two triangles. Click the check box to reveal the respective areas. Were you right? If not, what did you neglect to think of? Why does this relationship make sense?

What about the corresponding angles? What do you think is happening to them under this transformation? Why? Click the check box to reveal the angle measures of each triangle. Can you tell which measure goes with which angle? (That last question is rhetorical.)

So, what does a dilation do? In other words, what is the relationship between the preimage and the image under a dilation? Will this be true for other polygons? Why?

Finally, let's talk about Point P, the center of the dilation. How does moving P affect the figures? Is there a relationship between P and the vertices of the triangle, and if so, what do you think it is?

Finally, click the "Show Rays" check box. Were you surprised? Either way, I hope you found this activity interesting!