To understand how a negative scale factor works, let's first review what a scale factor represents in a dilation.
A dilation is a transformation that changes the size of a shape without altering its shape or orientation. The scale factor determines how much the shape is enlarged or reduced.
A positive scale factor greater than 1 enlarges the shape, while a positive scale factor between 0 and 1 reduces the shape.
On the other hand, a negative scale factor flips or reflects the shape about the center of dilation before enlarging or reducing it. This transformation can be visualized as a mirror image of the shape.
In the given problem, the scale factor is -2/3, which means that after reflecting the shape about the center of dilation, it will be reduced by a factor of 2/3.