Final answer:
The transformation of the points (10, -2) to (-2, -10) is a rotation around the origin, as the distance from each point to the origin remains consistent before and after the transformation.
The correct answer is D.
Step-by-step explanation:
The transformation of the points (10, -2) to (-2, -10) is described as a rotation around the origin of the coordinate system. This is because the distance of each original point from the origin (the length of the vector from the origin to the point) remains the same after transformation, which is a key characteristic of rotations.
For instance, if we calculate the distance of the point (10, -2) from the origin, we find √(10² + (-2)²) = √(100 + 4) = √104. The same distance will be found for the rotated point (-2, -10), which is √((-2)² + (-10)²) = √(4 + 100) = √104.