Chapter 11, Problem 29CR

To determine

To find: Vertices of each figure after a dilation.

Answer to Problem 29CR

Coordinates after dilation are

  $\begin{array}{l}F\text{'}\left(2.5,7.5\right)\\ G\text{'}\left(7.5,10\right)\\ H\text{'}\left(5,2.5\right)\end{array}$

Explanation of Solution

Given information:

  $\begin{array}{l}k=2.5\\ F=\left(1,3\right)\\ G=\left(3,4\right)\\ H=\left(2,1\right)\end{array}$

The dilation is $\left(x,y\right)\to \left(2.5x,2.5y\right)$ .

Multiply the coordinates of each vertex by $2.5$ .

  $\begin{array}{l}F\left(1,3\right)\to F\text{'}\left(2.5\left(1\right),2.5\left(3\right)\right)\\ \Rightarrow F\left(1,3\right)\to F\text{'}\left(2.5,7.5\right)\end{array}$

  $\begin{array}{l}G\left(3,4\right)\to G\text{'}\left(2.5\left(3\right),2.5\left(4\right)\right)\\ \Rightarrow G\left(3,4\right)\to G\text{'}\left(7.5,10\right)\end{array}$

  $\begin{array}{l}H\left(2,1\right)\to H\text{'}\left(2.5\left(2\right),2.5\left(1\right)\right)\\ \Rightarrow H\left(2,1\right)\to H\text{'}\left(5,2.5\right)\end{array}$

Therefore,

Coordinates after dilation are

  $\begin{array}{l}F\text{'}\left(2.5,7.5\right)\\ G\text{'}\left(7.5,10\right)\\ H\text{'}\left(5,2.5\right)\end{array}$

Graph of image is