Final answer:
The difference is that a scale factor of 0 shrinks the image to a single point at the origin, while a scale factor of 1 leaves the image size and shape unchanged.
Step-by-step explanation:
The difference between an image under a dilation centered at the origin with a scale factor of 0 and a scale factor of 1 is that at a scale factor of 0, the image would shrink to a single point at the origin, effectively disappearing. On the other hand, with a scale factor of 1, the image remains unchanged in size and shape, maintaining the original dimensions of the object being dilated. Dilation in mathematics refers to a transformation that resizes an object by a certain ratio which is defined by the scale factor. If the scale factor is greater than 1, the object enlarges (expands); if it is less than 1 (but greater than 0), the object reduces (contracts). Scale factor 0 is a special case leading to a degenerate image at the origin, while a scale factor of 1 implies no change at all, hence called an identity transformation.