Final answer:
To find the scale factor 'k' for a polygon whose perimeter changes from 12 units to 8 units, divide the new perimeter by the original perimeter, yielding a scale factor k = 8 / 12 = 2/3. The correct option is B. 2/3.
Step-by-step explanation:
The question is asking to find the scale factor 'k' used to dilate a polygon that decreases its perimeter from 12 units to 8 units. To find the scale factor, you can set up a proportion comparing the image's new perimeter to the original perimeter. Since perimeters scale directly with the scale factor in geometric figures, you can find 'k' by dividing the new perimeter by the original perimeter.
The original perimeter is 12 units, and the image's perimeter after dilation is 8 units. Therefore, you calculate the scale factor 'k' as follows:
k = new perimeter / original perimeter
= 8 / 12
= 2 / 3
The scale factor that transforms a perimeter of 12 units to a perimeter of 8 units is 2/3. Therefore, the correct option is B. 2/3.