Chapter 11.7, Problem 27STP

To determine

To find: Vertices of each figure after a dilation.

Answer to Problem 27STP

  $\begin{array}{l}P\text{'}\left(3,-3\right)\\ Q\text{'}\left(-6,18\right)\\ R\text{'}\left(12,3\right)\end{array}$

Explanation of Solution

Given information:

  $\begin{array}{l}k=3\\ P=\left(1,-1\right)\\ Q=\left(-2,6\right)\\ R=\left(4,1\right)\end{array}$

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

Multiply the coordinates of each vertex by $3$ .

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

  $\begin{array}{l}Q\left(-2,6\right)\to Q\text{'}\left(3\left(-2\right),3\left(6\right)\right)\\ \Rightarrow Q\left(-2,6\right)\to Q\text{'}\left(-6,18\right)\end{array}$

  $\begin{array}{l}R\left(4,1\right)\to R\text{'}\left(3\left(4\right),3\left(1\right)\right)\\ \Rightarrow R\left(4,1\right)\to R\text{'}\left(12,3\right)\end{array}$

Therefore,

Coordinates after dilation are

  $\begin{array}{l}P\text{'}\left(3,-3\right)\\ Q\text{'}\left(-6,18\right)\\ R\text{'}\left(12,3\right)\end{array}$