Chapter 11, Problem 17CR

To determine

To find: Graph the figure and its image.

Answer to Problem 17CR

Vertices of Figure after Translation are

  $\begin{array}{l}N\text{'}\left(8,1\right)\\ P\text{'}\left(5,7\right)\\ Q\text{'}\left(11,4\right)\end{array}$

Explanation of Solution

Given information:

Vertices of triangle are

  $\begin{array}{l}N\left(6,3\right)\\ P\left(3,9\right)\\ Q\left(9,6\right)\end{array}$

We need to translate $2$ units right and $2$ units down.

We need to translate $2$ units right and $2$ units down.

We can write translate as $\left(2,-2\right)$

  $\begin{array}{l}N\left(6,3\right)\to N\left(6,3\right)+\left(2,-2\right)\\ \Rightarrow N\left(6,3\right)\to N\text{'}\left(6+2,3-2\right)\\ \Rightarrow N\left(6,3\right)\to N\text{'}\left(8,1\right)\\ P\left(3,9\right)\to P\left(3,9\right)+\left(2,-2\right)\\ \Rightarrow P\left(3,9\right)\to P\text{'}\left(3+2,9-2\right)\\ \Rightarrow P\left(6,3\right)\to P\text{'}\left(5,7\right)\\ Q\left(9,6\right)\to Q\left(9,6\right)+\left(2,-2\right)\\ \Rightarrow Q\left(9,6\right)\to Q\text{'}\left(9+2,6-2\right)\\ \Rightarrow Q\left(9,6\right)\to Q\text{'}\left(11,4\right)\end{array}$

Therefore,

Vertices of Figure after Translation are

  $\begin{array}{l}N\text{'}\left(8,1\right)\\ P\text{'}\left(5,7\right)\\ Q\text{'}\left(11,4\right)\end{array}$

Graph of figure and its image is