Chapter 14.5, Problem 19WE

To determine

To graph the quadrilateral and its image and find the ratio of the perimeters and the areas of the two quadrilaterals.

Explanation of Solution

Given information:

The points of the quadrilateral are:

  $P\left(12,0\right),Q\left(0,15\right),R\left(-9,6\right)\text{ and }S\left(3,-9\right)$

The given dilation is $D_{O,\frac{2}{3}}$ .

Graph:

The quadrilateral and its image after dilation are:

  

Interpretation:

The ratio of the perimeter of the original quadrilateral to its image after dilation $D_{O,k}$ is $\left|k\right|$ times, so the ratio of the perimeters is $\frac{2}{3}$ .

The ratio of the area of the original quadrilateral to its image after dilation $D_{O,k}$ is $k^2$ times, so the ratio of the areas is $\frac{4}{9}$ .