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.

enter image description here

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?

  • $\begingroup$ Well, what's the size of $\theta$? $\endgroup$
    – Newb
    Commented Jul 13, 2014 at 0:37

1 Answer 1


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.

  • $\begingroup$ That's another way I've considered it, but how do you end up with a rounded curve when only one point moves? Wouldn't you end up with the original line except with that one point rotated at $\frac{\pi}{4}$? $\endgroup$
    – maogenc
    Commented Jul 13, 2014 at 14:35
  • $\begingroup$ That seems right to me. I thought the image was your own interpretation and not given. I dont see how one would easily map those lines to each other, exept something with complex numbers maybe $\endgroup$
    – Ragnar
    Commented Jul 13, 2014 at 14:37

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