Origin Dilations Investigation: Try and Guess!
What is a Dilation?
1. So far we have investigated rigid transformations. List the rigid transformations we have discussed, and explain what makes them "rigid"?
2. Without going ahead in the applet, and without knowing what a dilation is, why do you think we did not include dilations under "rigid transformations"?
Now that you have a thought about what makes a dilation not a "rigid transformation", let's investigate what a dilation is.
Exploration & Investigation Time!
Change the scale factor using the slider and write down anything you notice.
**Note: When I say anything I mean anything! It's okay to have general observations (like saying a parabola looks like a rainbow) but try to have some specific ones too (like saying a parabola only crosses the y-axis once).
***Sometimes GeoGebra will round numbers
Observation Reflection
3.. Did your observations stay true for any value of the slider? (If you are not sure, go back and try it!)
a. When the image was smaller than the pre-image? Bigger than the pre-image?
4. Look at your observations, is there any general rules about dilations that you think you can make? Why?
Test your rules!
I've copied the applet below. Move points Q, R, and/or P to make a triangle that looks different than in the previous applet.
Do your rules still work? Did you notice any new rules?
Compare with a partner or with a group!
5) Do you guys have any rules in common? Which ones?
6) Did your group/partner have a rule that was different than any of yours? Do their rules make sense to you? (If not, ask them about their rules.)
7) As a group/partners, compile a list of rules of what you guys have observed that makes a dilation a dilation, and explain why it is not a rigid transformation.
***Once every group has a list, we will compare all of our rules as a class!