Chapter 14.6, Problem 20WE

To determine

To find the coordinates of the image point.

Answer to Problem 20WE

The coordinates of the image point are $\left(-5,-1\right).$

Explanation of Solution

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

Calculation:

In coordinate terms;

For half- turn about the origin,

  $H_o:\left(x_1,y_1\right)\to \left(-x_1,-y_1\right)\mathrm{.....}\left(1\right)$

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

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

Use equation $\left(2\right)$$H_A:\left(1,1\right)\to \left(5,1\right)$

As the coordinates are $2$ unites left, and, the image of the coordinates will be $2$ units right .

  $\begin{array}{l}{H}_o:\left(5,1\right)\to \left(-5,-1\right)\\ \text{Therefore},H_{o}o{H}_a:\left(1,1\right)\to \left(-5,-1\right)\end{array}$

Draw the grid as shown below:

  

Thus, the coordinates of the image point are $\left(-5,-1\right).$