Chapter 14.6, Problem 17WE

To determine

To find the coordinates of the image point.

Answer to Problem 17WE

The coordinates of the image point are $\left(-3,-1\right).$

Explanation of Solution

Given information: Given coordinates of a point $A\left(3,1\right).$

Calculation:

In coordinate terms;

If the line of reflection is $x-$ axis then the reflection is $R_x:\left(x_1,y_1\right)\to \left(x_1,-y_1\right)\mathrm{.....}\left(1\right)$

And if the line of reflection is $x-$ axis then the reflection is $R_y:\left(x_1,y_1\right)\to \left(-x_1,y_1\right)\mathrm{.....}\left(2\right)$

Consider $R_x\text{ and }{R}_y$ are the reflection lines in a $x-y$ plane.

Where, $O$ is the origin and $A$ is a point with coordinates $\left(3,1\right).$

Use equation $\left(2\right),$$R_y:\left(3,1\right)\to \left(-3,1\right)\mathrm{.....}\left(2\right)$

Use equation $\left(1\right)$ , $R_x:\left(-3,1\right)\to \left(-3,-1\right)$

  $\text{Therefore},R_{x}o{R}_y:\left(3,1\right)\to \left(-3,-1\right).$

Draw the grid as shown below:

  

Thus, the coordinates of the image point are $\left(-3,-1\right).$