Chapter 11.7, Problem 7IP

To determine

To find: Vertices of each figure after a dilation.

Answer to Problem 7IP

  $\begin{array}{l}G\text{'}\left(0,4.5\right)\\ J\text{'}\left(3,0\right)\\ I\text{'}\left(6,1.5\right)\\ H\text{'}\left(1.5,9\right)\end{array}$

Explanation of Solution

Given information:

  $\begin{array}{l}k=1.5\\ G=\left(0,3\right)\\ J=\left(2,0\right)\\ I=\left(4,1\right)\\ H=\left(1,6\right)\end{array}$

The dilation is $\left(x,y\right)\to \left(4x,4y\right)$ .

Multiply the coordinates of each vertex by $4$ .

  $\begin{array}{l}G\left(0,3\right)\to G\text{'}\left(1.5\left(0\right),1.5\left(3\right)\right)\\ \Rightarrow G\left(0,3\right)\to G\text{'}\left(0,4.5\right)\end{array}$

  $\begin{array}{l}J\left(2,0\right)\to J\text{'}\left(1.5\left(2\right),1.5\left(0\right)\right)\\ \Rightarrow J\left(2,0\right)\to J\text{'}\left(3,0\right)\end{array}$

  $\begin{array}{l}I\left(4,1\right)\to I\text{'}\left(1.5\left(4\right),1.5\left(1\right)\right)\\ \Rightarrow I\left(4,1\right)\to I\text{'}\left(6,1.5\right)\end{array}$

  $\begin{array}{l}H\left(1,6\right)\to H\text{'}\left(1.5\left(1\right),1.5\left(6\right)\right)\\ \Rightarrow H\left(1,6\right)\to H\text{'}\left(1.5,9\right)\end{array}$

Therefore,

Coordinates after dilation are

  $\begin{array}{l}G\text{'}\left(0,4.5\right)\\ J\text{'}\left(3,0\right)\\ I\text{'}\left(6,1.5\right)\\ H\text{'}\left(1.5,9\right)\end{array}$

Graph of image is