Chapter 9.4, Problem 46HP

To determine

To find: The coordinates of $D^{″}$ is reflected over the y axis.

Answer to Problem 46HP

The coordinate of $D^{″}$ is $\left(-2,9\right)$ .

Explanation of Solution

Given:

If $\overline{CD}$ has the vertices $C\left(2,4\right)$ and $D\left(8,7\right)$ it is translated along the vector $\left(-6,2\right)$ .

Calculation:

Consider the coordinate of $D$ is $\left(8,7\right)$ .

The first step is to translate $\overline{CD}$ along $\langle -6,2\rangle$ as,

  $\begin{array}{l}\left(x,y\right)\to \left(x-6,y+2\right)\\ D\left(8,7\right)\to D^{\prime }\left(2,9\right)\end{array}$

Then, reflect the y axis as,

  $\begin{array}{l}\left(x,y\right)\to \left(-x,y\right)\\ D^{\prime }\left(2,9\right)\to D^{″}\left(-2,9\right)\end{array}$

Thus, the coordinate of $D^{″}$ is $\left(-2,9\right)$ .