Question

y reflection is trivially a composition of reflections. which of the following is true of rotations?
a. any rotation can be expressed as a composition of reflections across two lines whose intersection point is the center of rotation.
b. any rotation can be expressed as a composition of reflections across two perpendicular lines whose intersection point is the center of rotation.
c. any rotation can be expressed as a composition of reflections across three lines whose single intersection point is the center of rotation.
d. any rotation can be expressed as a composition of reflections across two parallel lines that are equidistant from the center of rotation.
slide reflection is a composition of a

followed by

as shown earlier, each of these can be expressed as a composition of reflections. it
oows that their composition, a glide reflection, can also be expressed as a composition of reflections. each type of rigid motion has now been considered, so the proof ism plete.

Explanation:

• For a rotation, the key property is that it can be represented as a composition of two reflections. The lines of reflection must intersect at the center of rotation.
• Option B is incorrect because the lines do not have to be perpendicular.
• Option C is incorrect as two reflections are sufficient, not three.
• Option D is incorrect as the lines must intersect (not be parallel) at the center of rotation.

Answer:

A. Any rotation can be expressed as a composition of reflections across two lines whose intersection point is the center of rotation.