Final answer:
Option D is incorrect because a composition of reflections across two intersecting lines results in a rotation, not a translation.
Step-by-step explanation:
The student's question pertains to the properties of geometric transformations, specifically reflections and the resultant transformations they produce when composed. To find the incorrect statement, let's examine each choice provided in the context of geometric transformations.
- Option A mentions that a composition of reflections across two intersecting lines is equivalent to a rotation, which is correct. If the lines intersect, the angle of rotation is twice the angle between the two lines.
- Option B says that a composition of reflections across three parallel lines is equivalent to one reflection, which is correct because reflecting across three parallel lines brings a point back to a line parallel to the original line, effectively acting as one reflection.
- Option C states that a composition of reflections across two parallel lines is equivalent to a translation, which is correct. The distance between the two parallel lines determines the magnitude of the translation, and the direction is perpendicular to the lines.
- Option D suggests that a composition of reflections across two intersecting lines is equivalent to a translation, which is incorrect. As established previously, this composition results in a rotation, not a translation.
Therefore, the statement that is NOT correct is Option D: A composition of reflections across two intersecting lines is equivalent to a translation.