Question

a certain mapping in the xy - plane has the following properties: - every point a on line l maps to itself. - every point p that isnt on l maps to point p such that l is the perpendicular bisector of pp. which transformation does the mapping define? choose 1 answer: a a translation b a reflection c a rotation

Explanation:

• Recall the definitions of translation, reflection, and rotation:
• Translation: Shifting all points by a fixed vector; no line of fixed points (except in trivial cases, but here line \( l \) has fixed points).
• Reflection: A transformation where a line (the line of reflection) is the perpendicular bisector of the segment joining a point and its image. Points on the line of reflection map to themselves.
• Rotation: Rotating around a point; only the center of rotation maps to itself (not a line of fixed points).
• The given mapping has a line \( l \) where all points on \( l \) map to themselves, and for points not on \( l \), \( l \) is the perpendicular bisector of \( PP' \). This matches the definition of a reflection over line \( l \).

Answer:

B. A reflection