Coordinate rotations and reflections

Imagine that you are playing with a toy car on a piece of paper. The paper has a big arrow pointing up, to show which way is up.

Now, if you turn the car to the left or right, you are doing something called a rotation. A rotation is when you turn something around a point, like how you might turn a merry-go-round at the playground. When you rotate your toy car, the arrow on the paper doesn't move - it's still pointing up - but the car is facing a different direction.

But what if you took the car and flipped it over? That's called a reflection. A reflection is like looking in a mirror - it's like making a copy of something, but with the left and right sides switched. If you put your toy car down on the paper again, and then flipped it over so it was facing the opposite direction, the arrow on the paper would still be pointing up, but the car would be facing the other way.

Now let's say you want to do both a rotation and a reflection at the same time. This might sound complicated, but it's actually pretty simple. If you rotate your toy car and then flip it over, that's the same as doing a different type of rotation. Specifically, it's a rotation about a line, which means you're rotating the car around an imaginary line rather than a single point.

So to summarize: a rotation is when you turn something around a point, a reflection is like looking in a mirror and making a copy with the left and right sides switched, and a rotation about a line is when you rotate something around an imaginary line. All of these things can help you change the way an object is facing without actually moving it from one place to another.