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:

Step1: Recall transformation definitions

• Translation: Shifts points without rotation/reflection, no line of symmetry.
• Reflection: A transformation where a line (line of reflection) is the perpendicular bisector of segments joining pre - image and image points. Points on the line map to themselves.
• Rotation: Turns points around a center, no line that is perpendicular bisector for all non - center points.

Step2: Match with given mapping

The mapping has a line \(\ell\) where points on \(\ell\) map to themselves, and for other points \(P\), \(\ell\) is the perpendicular bisector of \(PP'\). This matches the definition of a reflection. It does not match translation (no shifting pattern with a line of self - mapping) or rotation (no center - based turning pattern here).

Answer:

B. A reflection