Final answer:
The rule (x, y) → (2x, 2y) describes a dilation in mathematics, where each point is scaled by a factor of 2 from a center point, resulting in an enlarged figure that maintains the same shape as the original.
Step-by-step explanation:
The transformation rule given as (x, y) → (2x, 2y) represents a dilation or enlargement transformation in mathematics. In such a transformation, each point of the original figure, or pre-image, is moved along a straight line that connects it to a fixed point called the center of dilation. This line is stretched or shrunk by a scale factor, which, in this case, is 2. The result is a figure that is proportionally similar to the original, with its size changed by the scale factor. Applying this rule to any coordinate (x, y), the resulting image coordinate becomes (2x, 2y), which means each x and y coordinate is multiplied by 2, effectively doubling the distance from the center of dilation, leading to an image twice the size of the original.