Question

a certain mapping in the xy-plane has the following properties: - for the point a, the image a is at the same point as a. - a point p that is not at a maps to a point p clockwise along the circumference of a circle centered at a and with a radius of ap. - m∠pap = θ. which transformation does the mapping define? choose 1 answer: a a translation b a reflection c a rotation

Explanation:

• Translation: Moves points without rotation/reflection, but here there's a rotational angle (\(\theta\)) around point \(A\), so not translation.
• Reflection: Flips over a line, but this mapping is along a circle (rotational) with a central angle, not a flip.
• Rotation: A rotation about a point (here, \(A\)) by an angle (\(\theta\)) maps a point \(P\) to \(P'\) on the circle centered at \(A\) with radius \(AP\), matching the given properties (fixed point \(A\), rotational angle \(\angle PAP'=\theta\), and circular mapping).

Answer:

C. A rotation