Chapter 14, Problem 25CT

a.

To determine

Tofind: the image of the slope line under the reflection in the x -axis.

Answer to Problem 25CT

The slope of the image of the line is $-2$ under the reflection in the x -axis .

Explanation of Solution

Given information:

Line has slope $2$ .

Calculation: the slope of the image of the line is $-2$ , because reflect the line in the x -axis,

Then the slope of the line must be $-2$ .

b.

To determine

To find: the image of the slope of the line under the reflection in the line $y=x$ .

Answer to Problem 25CT

The slope of the image of the line is $2$ under the reflection in the line $y=x$ .

Explanation of Solution

Given information:

Line has slope $2$ .

Calculation: when the line reflect in the line $y=x$ , the slope of the line remain constant.

Thus, the slope of the image of the line is $2$ .

c.

To determine

To find: the image of the slope of the line under the dilation $D_{O,3}$ .

Answer to Problem 25CT

The slope of the image of the line is $6$ under the dilation $D_{O,3}$ .

Explanation of Solution

Given information:

Line has slope $2$ .

Calculation: when dilation is $D_{O,3}$ , then multiply the slope by $3$ .

Thus, the slope of the slope of the line is $6$ .