Chapter 12.7, Problem 16E

To determine

To draw the image after dilating its coordinates.

Answer to Problem 16E

The images after dilations are:

  

Explanation of Solution

Given information:

The following figure is given:

  

The figure is to be dilated using the following scale factors:

  $\frac{1}{2},1\frac{1}{2},2$

Calculation :

The coordinates after dilating the coordinates from the given figure using scale factor $\frac{1}{2}$ :

  $\begin{array}{l}\left(-1,6\right)\to \left(-\frac{1}{2},3\right)\\ \left(1,6\right)\to \left(\frac{1}{2},3\right)\\ \left(2,2\right)\to \left(1,1\right)\\ \left(-2,2\right)\to \left(-1,1\right)\\ \left(-1,0\right)\to \left(-\frac{1}{2},0\right)\\ \left(1,0\right)\to \left(\frac{1}{2},0\right)\end{array}$

The image after dilation using scale factor $\frac{1}{2}$ is:

  

The coordinates after dilating the coordinates from the given figure using scale factor $1\frac{1}{2}$ :

  $\begin{array}{l}\left(-1,6\right)\to \left(-1\frac{1}{2},9\right)\\ \left(1,6\right)\to \left(1\frac{1}{2},9\right)\\ \left(2,2\right)\to \left(3,3\right)\\ \left(-2,2\right)\to \left(-3,3\right)\\ \left(-1,0\right)\to \left(-1\frac{1}{2},0\right)\\ \left(1,0\right)\to \left(1\frac{1}{2},0\right)\end{array}$

The image after dilation using scale factor $1\frac{1}{2}$ is:

  

The coordinates after dilating the coordinates from the given figure using scale factor $2$ :

  $\begin{array}{l}\left(-1,6\right)\to \left(-2,12\right)\\ \left(1,6\right)\to \left(2,12\right)\\ \left(2,2\right)\to \left(4,4\right)\\ \left(-2,2\right)\to \left(-4,4\right)\\ \left(-1,0\right)\to \left(-2,0\right)\\ \left(1,0\right)\to \left(2,0\right)\end{array}$

The image after dilation using scale factor $2$ is: