Exploring Dilations: Part 1

Interact with the app below for a few minutes. Have fun exploring! (LARGE POINTS, the slider, and Lisa's pic are moveable.)

What do you notice? What do you wonder? Notice anything interesting? Describe any phenomena you see (as best as you can) in the space below.

In the app above, Lisa's pic is said to be dilated about point A by a scale factor k. What does a dilation seem to do to Lisa's original pic? What can it do? Describe.

In the app below, use the line tool to construct line BC and line B'C'. Then move A, B, and C around a bit. Move the slider as well. What seems to be true about the two lines?

Use the tool(s) of GeoGebra to prove your assertion is true. Then explain how what you did shows your claim is indeed true.

Can you prove your assertion is true another way? Try to do so!