Question

find the scale factor of the dilation. then tell whether the dilation is a reduction or an enlargement. the scale factor is (square). the image is a(n) (square).

Explanation:

Step1: Determine the scale factor

The scale factor \(k\) of a dilation is given by the ratio of the distance from the center of dilation to a point on the image (\(CD\)) to the distance from the center of dilation to the corresponding point on the pre - image (\(CB\)).
We know that \(CD = 24\) and \(CB=9\). The scale factor \(k=\frac{CD}{CB}\).

$$k = \frac{24}{9}=\frac{8}{3}$$

Step2: Determine if it is a reduction or an enlargement

Since the scale factor \(k=\frac{8}{3}\approx2.67> 1\), when the scale factor \(k>1\), the dilation is an enlargement.

Answer:

The scale factor is \(\frac{8}{3}\). The image is an enlargement.