What is the scale factor if a shape is dilated to half its original size?

When a shape is dilated to half its original size, the scale factor represents the ratio of the new size to the original size. In this case, if the new size is half the original size, the transformation can be expressed mathematically as a ratio.

When we say a shape is half its original size, we can denote the original size as 1 (or 100%) and the new size as 1/2. To find the scale factor, you take the new size (1/2) and divide it by the original size (1):

Scale factor = new size / original size = (1/2) / 1 = 1/2.

This calculation clearly shows that the scale factor is 1/2, indicating that the dimensions of the shape are reduced to half. The correct choice reflects this understanding of the concept of dilation in geometry, confirming that the shape is decreased in size by a factor of 1/2.