Question

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

Explanation:

Step1: Find the scale factor

The scale factor \(k\) of a dilation is given by the formula \(k=\frac{\text{distance from center of dilation to a point on the image}}{\text{distance from center of dilation to the corresponding point on the pre - image}}\).
Here, the distance from the center of dilation \(C\) to a point on the image \(CP'=24\), and the distance from the center of dilation \(C\) to the corresponding point on the pre - image \(CP = 9\). So, \(k=\frac{24}{9}=\frac{8}{3}\)

Step2: Determine if it is an enlargement or a reduction

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

Answer:

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