MHB How does rigid transformation and dilation help with learning Geometry?

[cbarker1]

Dear Everybody,

I am in the process of relearning high school geometry through Khan Academy. I am current an graduated undergraduate student in mathematics. I am doing this because geometry is one of my weakest subject in mathematics. Second reason is that I want to reason out a problem geometrically. I also want to relearn my university level geometry textbook. I have a hard time with spatial reasoning in general. I am wondering why does learning the rigid transformations and dilations and symmetries help with learning high school geometry.Thanks,

cbarker1

 

[topsquark]

Say that we have a sphere that isn't centered on the origin. The equation for the sphere isn't too bad but if you want to talk about symmetries it is easier to translate the center of the sphere to the origin. Dilation (at least in Physics) can be used, where possible, to make the numbers a bit more convenient.

-Dan