Conjugating Transformations
Conjugating a Rotation
To determine what happens to a point, P, when we rotate it about a point, C, that is not at the origin of the Cartesian plane, O; we can first translate C to O, then rotate about O, then undo the translation. See how this works in the example below.
Conjugating a Reflection
Now, let's try using conjugation to determine what happens when we reflect over a line that does not pass through the origin.
Step 1: Translate the line to pass through the origin
Step 2: Rotate to align with the x-axis
To rotate, we use a rotation around the origin by where .