Chapter 9.4, Problem 26PPS

To determine

To find: The graph and its mirror image.

Answer to Problem 26PPS

The graph and its mirror image is shown in Figure 1.

Explanation of Solution

Given:

Consider the given diagram.

  

Calculation:

For x-axis,

  $\begin{array}{l}\left(x,y\right)\to \left(x,-y\right)\\ A\left(3,0\right)\to A\text{'}\left(3,0\right)\\ B\left(4,1\right)\to B\text{'}\left(4,-1\right)\\ C\left(5,4\right)\to C\text{'}\left(4,-5\right)\end{array}$

And,

  $\begin{array}{l}D\left(6,9\right)\to D\text{'}\left(6,-9\right)\\ E\left(0,9\right)\to E\text{'}\left(0,-9\right)\\ F\left(1,4\right)\to F\text{'}\left(1,-4\right)\\ G\left(2,1\right)\to G\text{'}\left(2,-1\right)\end{array}$

Write the equation of line.

  $y=-{\left(x-3\right)}^2$

For y-axis,

  $\begin{array}{l}\left(x,y\right)\to \left(-x,y\right)\\ A\text{'}\left(3,0\right)\to A\text{'}\text{'}\left(3,0\right)\\ B\text{'}\left(4,-1\right)\to B\text{'}\text{'}\left(-4,-1\right)\\ C\text{'}\left(4,-5\right)\to C\text{'}\text{'}\left(-4,-5\right)\end{array}$

And,

  $\begin{array}{l}D\text{'}\left(6,-9\right)\to D\text{'}\text{'}\left(-6,-9\right)\\ E\text{'}\left(0,-9\right)\to E\text{'}\text{'}\left(0,-9\right)\\ F\text{'}\left(1,-4\right)\to F\text{'}\text{'}\left(-1,-4\right)\\ G\text{'}\left(2,-1\right)\to G\text{'}\text{'}\left(-2,-1\right)\end{array}$

Write the equation of line.

  $y=-{\left(x+3\right)}^2$

The required diagram is shown below:

  

Figure 1

Thus, the graph and its mirror image is shown in Figure 1.