Chapter 9.4, Problem 1CYU

To determine

To plot: The graph of $\Delta CDE$ and its image after the indicated glide reflection.

Answer to Problem 1CYU

The required figure is shown in figure (3).

Explanation of Solution

Given:

The vertices of $\Delta CDE$ are $C\left(-5,-1\right)$ , $D\left(-2,-5\right)$ , and $E\left(-1,-1\right)$ .

Calculation:

Plot the triangle with the help of given vertices as follows.

  

Figure (1)

Since, the $\Delta CDE$ has the vertices $C\left(-5,-1\right)$ , $D\left(-2,-5\right)$ , and $E\left(-1,-1\right)$ , and the translation is along $\left(4,0\right)$ .

So, the translation x-coordinate will increase by 4 units of the original value.

Add 4 units to each z-coordinate as $\left(x,y\right)\to \left(x+4,y\right)$ .

So, the vertices of translated $\Delta C\text{'}D\text{'}E\text{'}$ are as follows.

  $\begin{array}{l}C\left(-5,-1\right)\to C\text{'}\left(-1,-1\right)\\ D\left(-2,-5\right)\to D\text{'}\left(2,-5\right)\\ E\left(-1,-1\right)\to E\text{'}\left(3,-1\right)\end{array}$

So, the triangle $\Delta C\text{'}D\text{'}E\text{'}$ is as follows.

  

Figure (2)

Since, the $\Delta C\text{'}D\text{'}E\text{'}$ has the vertices $C\text{'}\left(-1,-1\right)$ , $D\text{'}\left(2,-5\right)$ , and $E\text{'}\left(3,-1\right)$ .

The reflection is in the x-axis, so the reflected y-coordinate will have opposite sign of the original value as $\left(x,y\right)\to \left(x,-y\right)$ .

The vertices of the triangle $\Delta C\text{'}\text{'}D\text{'}\text{'}E\text{'}\text{'}$ are as follows.

  $\begin{array}{l}C\text{'}\left(-1,-1\right)\to C\text{'}\text{'}\left(-1,1\right)\\ D\text{'}\left(2,-5\right)\to D\text{'}\text{'}\left(2,5\right)\\ E\text{'}\left(3,-1\right)\to E\text{'}\text{'}\left(3,1\right)\end{array}$

So, the triangle $\Delta C\text{'}\text{'}D\text{'}\text{'}E\text{'}\text{'}$ is as follows.

  

Figure (3)

Therefore, the required figure is shown in figure (3).