Question

identifying dilations
what scale factor that maps the preimage onto the image?
k =

Explanation:

Step1: Determine preimage and image heights

Assume each grid square has side length 1. The preimage (larger trapezoid) has a height (vertical length) of, say, 8 units (from y - axis related grid). The image (smaller trapezoid) has a height of 4 units.

Step2: Calculate scale factor \( k \)

The scale factor \( k \) for dilation is the ratio of the image length to the preimage length. So \( k=\frac{\text{Image Height}}{\text{Preimage Height}}=\frac{4}{8}=\frac{1}{2} \). (We can also check horizontal lengths: Preimage top base length, say 2 units, image top base length 1 unit, \( \frac{1}{2} \) as well.)

Answer:

\( \frac{1}{2} \)