Question

which letter can be mapped onto itself by a $180^{circ}$ rotation about its center?

choose the correct answer below

y n
a e

Explanation:

Step1: Recall 180° rotation

A 180° rotation about a center means that each point \((x,y)\) on the figure maps to \((-x,-y)\) (in a coordinate system centered at the figure's center). We need to check which letter looks the same after this rotation.

Step2: Analyze each letter

• Letter Y: After 180° rotation, the top part (the two arms and the stem) will point down, and it won't look like Y anymore.
• Letter A: After 180° rotation, the triangular part will be inverted, and it won't look like A.
• Letter N: When we rotate N 180° about its center, the vertical lines and the diagonal part will align such that it still looks like N.
• Letter E: After 180° rotation, the horizontal lines will be inverted, and it won't look like E.

Answer:

N (the option with the letter N)