Final answer:
A dilation with a scale factor at the origin multiplies each coordinate by the scale factor, expanding or contracting the shape accordingly.
Step-by-step explanation:
The rule that describes a dilation with a scale factor and the center of dilation at the origin in a coordinate system involves multiplying the coordinates (x, y) of each point by the scale factor to produce the image point (x', y'). If the scale factor is greater than 1, the shape expands; if it's between 0 and 1, the shape contracts. For instance, with a scale factor of 2, a point at (3, 4) would be mapped to (6, 8) after the dilation.