Chapter 14.2, Problem 20CE

a.

To determine

To explain that an isometry preserves distance.

Answer to Problem 20CE

Since, the isometry figures are always congruent that means it preserves its dimensions therefore the distance is also preserved. Hence, a statement can be made that an isometry preserves distance.

Explanation of Solution

Given information:

The given statement is that an isometry preserves distance.

Since, the isometry figures are always congruent that means it preserves its dimensions therefore the distance is also preserved. Hence, a statement can be made that an isometry preserves distance.

b.

To determine

To explain that area is invariant under a reflection.

Answer to Problem 20CE

Under a reflection distance is preserved, angles are mapped as congruent and shape is also preserved so the area also remains unchanged.

Explanation of Solution

Given information:

The given statement is thatarea is invariant under a reflection.

Under a reflection distance is preserved, angles are mapped as congruent and shape is also preserved so the area also remains unchanged therefore it can be stated that area is invariant under a reflection.

c.

To determine

To explain that orientation is not invariant under a reflection.

Answer to Problem 20CE

Explanation of Solution

Given information:

The given statement is that orientation is not invariant under a reflection.

Orientation is not invariant under reflection can be better explained by a figure representing reflection.

Here it is clearly visible that the orientation of the triangle changes by $180°$ . Since an example of variation in orientation under reflection is shown therefore it can be stated that orientation is not invariant under a reflection.