Chapter 14.6, Problem 23WE

To determine

To find the coordinates of the image point.

Answer to Problem 23WE

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

Explanation of Solution

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

Calculation:

Calculation:

A rotation is a transformation suggested by rotate 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 $\left(p\right)$ .

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 $\left(-1,-1\right)$ .

Now as rotation is about the center $O$ is clock wise ,

Therefore, ${\Re }_{o,-90}:\left(-1,-1\right)\to \left(-1,1\right)$

Now, as the rotation is about the center $O$ , ${\Re }_{A,90}:\left(-1,1\right)\to \left(3,-3\right)$

  $\text{Therefore},{\Re }_{{}_{A,90}}o{\Re }_{{}_{o,-90}}:\left(-1,-1\right)\to \left(3,-3\right)$

Draw the grid as shown below:

  

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