Question

layla tried to define a rotation.

• for the center point c, the image c is at the same point as c.
• for a point p that is not at c, a counterclockwise rotation of θ about point c creates point p, such that m∠pcp = θ.

what mistake did layla make in her definition of a rotation?
choose 1 answer:
a layla needed to include the distance between each point p and its image p.
b cp must be perpendicular to cp.
c the lengths of \\(\overline{cp}\\) and \\(\overline{cp}\\) must be equal.
d layla did not make a mistake.

Explanation:

A rotation in geometry preserves the distance from the center of rotation to each point and its image. Layla's definition mentions the angle but not that \( CP = CP' \) (lengths of segments from center to point and its image must be equal). Option A is incorrect as rotation doesn't require including the distance between \( P \) and \( P' \) (that's not a key part of rotation definition). Option B is wrong because \( CP \) and \( CP' \) are only perpendicular for 90° rotations, not all. Option D is wrong as there is a mistake. So the correct answer is C.

Answer:

C. The lengths of \(\overline{CP}\) and \(\overline{CP'}\) must be equal.