Chapter 14.6, Problem 14WE

a.

To determine

To identify the invariant under the composite of reflection.

Answer to Problem 14WE

The properties which are invariant under the composite of reflection and a dilation is $a,b\text{ and }c.$

Explanation of Solution

Given a composite of reflection and dilation.

Calculation:

Check whether the distance is invariant under a composite of two reflections.

A the composite ofreflections in two intersecting lines are a rotation about the point of intersection of

the two lines . The measure of the angle of rotation is twice the measure of the angle from the first line

of reflection to the second.

And exceptthe half-turn, in rotation only the orientation is not invariant therefore, the distance is

Invariant under a composite of two reflections.

b.

To determine

To identify the invariant under the composite of reflection.

Answer to Problem 14WE

The properties which are invariant under the composite of reflection and a dilation is $a,b\text{ and }c.$

Explanation of Solution

Given a composite of reflection and dilation.

Calculation:

Check whether the angle measure isinvariant under a composite of two reflections..

The composite ofreflections in two intersecting lines are a rotation about the point of intersection of the two lines. The measure of the angle of rotation is twice the measure of the angle from the first line of reflection to the second.

And except the half-turn, in rotation only the orientation is not invariant therefore, the angle measure is

Invariant under a composite of two reflections.

c.

To determine

To identify the invariant under the composite of reflection.

Answer to Problem 14WE

The properties which are invariant under the composite of reflection and a dilation is $a,b\text{ and }c.$

Explanation of Solution

Given a composite of reflection and dilation.

Calculation:

Check whether the area isinvariant under a composite of two reflections.

A the composite ofreflections in two intersecting lines are a rotation about the point of intersection of the two lines . The measure of the angle of rotation is twice the measure of the angle from the first line of reflection to the second.

And except the half-turn, in rotation only the orientation is not invariant therefore, the area is

Invariant under a composite of two reflections.