Final answer:
A -90 degrees rotation of a point in a coordinate system results in a new location for the point, which does not map to the original line, because rotations preserve distances and change directions, making them isometric transformations.
Step-by-step explanation:
When discussing rotations in a coordinate system, it's important to understand that a rotation transformation will change the positional coordinates of a point without altering the distances between points. In the context of a -90 degrees rotation, every point that gets rotated will move to a new location while maintaining the same distance from the origin, effectively mapping to a new line, not onto itself. This is because rotations in a coordinate system are designed to preserve distances, which is a characteristic known as being an isometric transformation.
If every point on a straight line rotated by -90 degrees were to map onto itself, that would mean the rotational transformation has not occurred since the points would have not changed position. Additionally, since the rotation is about the origin, the new position of a point will have the same 'distance' or magnitude of the vector from the origin, but the direction will be different.
Considering a more physics-related concept, we can also contrast this with a scenario where a vector representing angular momentum is crossed with a parallel vector and results in zero because they are parallel. This is not the case with rotation, as the vectors' directions change, they do not stay parallel after rotation.