Question

any 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.

Explanation:

• A rotation can be thought of as a composition of two reflections. When we reflect a figure across one line and then across another line that intersects the first line, the result is a rotation. The point of intersection of these two lines is the center of rotation.
• Option B is incorrect because two reflections are sufficient for a rotation, not three.
• Option C is incorrect as three reflections are not needed for a general rotation.
• Option D is incorrect because for a rotation, the lines of reflection should intersect (not be parallel). Parallel lines of reflection result in a translation, not a rotation.

Answer:

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