1) Each point on the coordinate plane is rotated $\theta$ degrees about the origin.
2) Each point $P$ with the coordinates $(x,y)$ is rotated $\frac{\pi}{4}$ radians about the origin.
The answer says rotation 2 "defines some strange transformation that doesn't preserve angle measures or segment lengths."
I don't see how this rotation is different than the first one and how the second rotation causes the weird transformation. Could someone provide a more detailed explanation?
I have two interpretations:
The first transformation clearly is just a rotation around the origin of the entire plane with angle $\theta$.
The second transformation could be a rotation around the origin of the entire plane with angle $\frac \pi4$. But when $x$ en $y$ are given, the second transformation only moves (rotates) only one point of the plane, and thus lengths are not preserved.