Chapter 14.6, Problem 24WE

To determine

To find the coordinates of the image point.

Answer to Problem 24WE

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

Explanation of Solution

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

Calculation:

Calculation:

A transformation related to similarity rather than congruence is called a dilation.

The dilation $D_{0,k}$ has center $O$ and non-zero scale factor $K$ .

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 $\left(3,0\right).$

As the scalar factor of the first dilation is $4$ ,and the center of dilation is the point $O$ .

Therefore, $D_{A,4}:\left(3,0\right)\to \left(3,-3\right)$

As the scalar factor of the second dilation is $-\frac{1}{3}$ ,and the center of dilation is the point $O$ .

  $D_{0,-\frac{1}{3}}:\left(3,-3\right)\to \left(-1,1\right)$

  $\text{Therefore},D_{0,-\frac{1}{3}}o{D}_{A,4}:\left(3,0\right)\to \left(-1,1\right)$

Draw the grid as shown below:

  

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