Chapter 11, Problem 27CR

To determine

To find: Vertices of each figure after a dilation.

Answer to Problem 27CR

Coordinates after dilation are

  $\begin{array}{l}Q\text{'}\left(-6,9\right)\\ R\text{'}\left(3,6\right)\\ S\text{'}\left(9,-3\right)\\ T\text{'}\left(-6,-6\right)\end{array}$

Explanation of Solution

Given information:

  $\begin{array}{l}k=3\\ Q=\left(-2,3\right)\\ R=\left(1,2\right)\\ S=\left(3,-1\right)\\ T=\left(-2,-2\right)\end{array}$

The dilation is $\left(x,y\right)\to \left(3x,3y\right)$ .

Multiply the coordinates of each vertex by $3$ .

  $\begin{array}{l}Q\left(-2,3\right)\to Q\text{'}\left(3\left(-2\right),3\left(3\right)\right)\\ \Rightarrow Q\left(-2,3\right)\to Q\text{'}\left(-6,9\right)\end{array}$

  $\begin{array}{l}R\left(1,2\right)\to R\text{'}\left(3\left(1\right),3\left(2\right)\right)\\ \Rightarrow R\left(1,2\right)\to R\text{'}\left(3,6\right)\end{array}$

  $\begin{array}{l}S\left(3,-1\right)\to S\text{'}\left(3\left(3\right),3\left(-1\right)\right)\\ \Rightarrow S\left(3,-1\right)\to S\text{'}\left(9,-3\right)\end{array}$

  $\begin{array}{l}T\left(-2,-2\right)\to T\text{'}\left(3\left(-2\right),3\left(-2\right)\right)\\ \Rightarrow T\left(-2,-2\right)\to T\text{'}\left(-6,-6\right)\end{array}$

Therefore,

Coordinates after dilation are

  $\begin{array}{l}Q\text{'}\left(-6,9\right)\\ R\text{'}\left(3,6\right)\\ S\text{'}\left(9,-3\right)\\ T\text{'}\left(-6,-6\right)\end{array}$

Graph of image is