Chapter 6.8, Problem 17PPS

To determine

To find: The scale factor of the dilation and classify it as an enlargement or a reduction.

Answer to Problem 17PPS

The scale factor is $\frac{2}{3}$ and it is reduction

Explanation of Solution

Given information:

Quadrilateral $A^{\prime }{B}^{\prime }{C}^{\prime }{D}^{\prime }$ is a dilation of quadrilateral $ABCD$ .

Calculation:

In the dilation, both figures are similar.

Corresponding sides are in constant ratio.

  $\frac{D^{\prime }{C}^{\prime }}{DC}=\frac{2}{3}$ .

Scale factor is $\frac{2}{3}<1$ .

The dilated figure is smaller than the original one as scale factor is less than one.

Hence, the scale factor is $\frac{2}{3}$ and it is reduction.