Chapter 14.6, Problem 19WE

To determine

To find the coordinates of the image point.

Answer to Problem 19WE

The coordinates of the image point are $\left(9,2\right).$

Explanation of Solution

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

Calculation:

In coordinate terms;

For half- turn about the orgin, $H_o:\left(x_1,y_1\right)\to \left(-x_1,-y_1\right)\mathrm{.....}\left(1\right)$

And if the line of reflection is $y-$ 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 $xy-$ plane.

Where, $O$ is the origin and $A$ is a point with coordinates $\left(3,1\right)$ and another point of the coordinates $\left(3,0\right)$ .

Use equation $\left(2\right)$

  $H_o:\left(3,0\right)\to \left(-3,0\right)$

As the coordinates are $6$ unites left, and $1$ unit down, the image of the coordinates will be $6$ units right and $1$ unit up, $H_A:\left(-3,0\right)\to \left(9,2\right)$

  $\text{Therefore},H_{A}o{H}_o:\left(3,0\right)\to \left(9,2\right)$

Draw the grid as shown below:

  

Thus, the coordinates of the image point are $\left(9,2\right).$