Chapter 14.6, Problem 21WE

To determine

To find the coordinates of the image point.

Answer to Problem 21WE

The coordinates of the image point are $\left(4,-8\right).$

Explanation of Solution

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

Calculation:

Calculation:

In coordinate terms;

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

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

Where, $O$ is the scalar factor of the dolinas $\left(2,4\right)$ and center point of the dilation is $O$ .

Use equation $\left(2\right)$

  $D_o:\left(2,4\right)\to \left(4,8\right)$

Now as the second tarnation is the reflection with respect to the $x-$ axis.

  $R_x:\left(4,8\right)\to \left(4,-8\right)$

  $\text{Therefore},R_{x}o{D}_O:\left(2,4\right)\to \left(4,-8\right)$

Draw the grid as shown below:

  

Thus, the coordinates of the image point are $\left(4,-8\right).$