To solve the question about the transformation of a parallelogram according to the rule [tex]\((x, y) \rightarrow (x, y)\)[/tex], let's analyze what this transformation implies.
1. Understanding the Transformation Rule: The rule [tex]\((x, y) \rightarrow (x, y)\)[/tex] indicates that every point [tex]\((x, y)\)[/tex] in the parallelogram is mapped to itself. This means that there is no change in the coordinates of any point in the parallelogram.
2. Rotations and Their Effects: Different rotations have distinct effects on the coordinates of points:
- [tex]\( R_{0,90^{\circ}} \)[/tex]: Rotating a shape by 90 degrees around the origin rotates each point to a new position, effectively changing the coordinates.
- [tex]\( R_{0,180^{\circ}} \)[/tex]: Rotating by 180 degrees around the origin also changes the coordinates of each point, flipping them to the opposite quadrants.
- [tex]\( R_{0,270^{\circ}} \)[/tex]: Similarly, rotating by 270 degrees repositions all points, changing the coordinates again.
- [tex]\( R_{0,360^{\circ}} \)[/tex]: Rotating by 360 degrees is a full circle rotation, which brings every point back to its original position. Thus, the coordinates remain unchanged.
3. Conclusion Based on the Transformation Rule: Since the transformation [tex]\((x, y) \rightarrow (x, y)\)[/tex] does not change the coordinates of any point, the transformation must be the one that maps each point to itself. This corresponds to a full rotation of 360 degrees.
Therefore, the correct way to state this transformation is:
[tex]\[ R_{0,360^{\circ}} \][/tex]
So, the correct answer is:
[tex]\[ R_{0,360^{\circ}} \][/tex]
