Chapter 14.6, Problem 22WE

To determine

To find the coordinates of the image point.

Answer to Problem 22WE

The coordinates of the image point are $\left(-1,2\right).$

Explanation of Solution

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

Calculation:

A rotation is a transformation suggested by rotates a paddle wheel.

When the wheel moves, each paddle rotates to a new position. When the wheel stops, the new position of a paddle $\left(p^{\prime }\right)$ can be referred to mathematically as the image of the initial position of the paddle $\left(p\right)$ .

In coordinates terms; $F$

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

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

Where, $O$ is the origin and a point of the coordinates $\left(-2,1\right)$ .

Use equation $\left(1\right)$

  $R_y:\left(-2,1\right)\to \left(2,1\right)$

Now as rotation is about the center $O$ , ${\Re }_{o,90}:\left(2,1\right)\to \left(-1,2\right)$

  $\text{Therefore},{\Re }_{o,90}o{R}_y:\left(-2,1\right)\to \left(-1,2\right).$

Draw the grid as shown below:

  

Thus, the coordinates of the image point are $\left(-1,2\right).$