MathDB
Coordinate Plane

Source: 2022 AMC 10A P18 / 2022 AMC 12A P18

November 11, 2022
AMCAMC 10AMC 122022 AMC 10a2022 AMC 12A2022 AMCtransformations

Problem Statement

Let TkT_k be the transformation of the coordinate plane that first rotates the plane kk degrees counterclockwise around the origin and then reflects the plane across the yy-axis. What is the least positive integer nn such that performing the sequence of transformations transformations T1,T2,T3,,TnT_1, T_2, T_3, \dots, T_n returns the point (1,0)(1,0) back to itself?
<spanclass=latexbold>(A)</span>359<spanclass=latexbold>(B)</span>360<spanclass=latexbold>(C)</span>719<spanclass=latexbold>(D)</span>720<spanclass=latexbold>(E)</span>721<span class='latex-bold'>(A) </span> 359 \qquad <span class='latex-bold'>(B) </span> 360\qquad <span class='latex-bold'>(C) </span> 719 \qquad <span class='latex-bold'>(D) </span> 720 \qquad <span class='latex-bold'>(E) </span> 721