Final answer:
To create a smaller polygon on a coordinate grid with the origin as the center of dilation, the scale factor must be between 0 and 1, specifically less than 1.
Step-by-step explanation:
To create a smaller polygon from a dilated polygon on a coordinate grid using the origin as the center of dilation, the correct scale factor would be one that is less than 1. This would mean the option B) The polygon will be dilated by a scale factor between 0 and 1 is the correct choice. A scale factor smaller than 1 will reduce the size of the polygon proportionally. Therefore, to dilate a polygon to create a smaller similar figure, each vertex of the original polygon is moved closer to the origin by a factor that is a fraction of its original distance.
Consider a simple example: If we have a square with vertices at (2,2), (2,-2), (-2,-2), and (-2,2) and we choose a scale factor of 1/2, the dilated square will have vertices at (1,1), (1,-1), (-1,-1), and (-1,1), thus creating a smaller square.