Question

What is 4,1 after a rotation of 180 degrees clockwise around the origin

Answer 1

Rotating the point
`(x,y)` 180 degrees around the origin in any direction will cause the following transformation:

`(x,y)\mapsto (-x,-y)`

Note that, since 180 is half a turn, it doesn't matter if you rotate clockwise or counter clockwise, since you'll end up at the antipode of your starting point anyway.