2022 AMC 12A Problems/Problem 18
Revision as of 21:32, 11 November 2022 by Stevenyiweichen (talk | contribs) (→Video Solution by Professor Chen Education Palace)
Contents
Problem
Let be the transformation of the coordinate plane that first rotates the plane
degrees counter-clockwise around the origin and then reflects the plane across the
-axis. What is the least positive
integer
such that performing the sequence of transformations
returns the point
back to itself?
Solution
Let be the point
.
Starting with , the sequence goes
We see that it takes turns to downgrade the point by
. Since the fifth point in the sequence is
, the answer is
Video Solution
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
See also
2022 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 17 |
Followed by Problem 19 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
2022 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 17 |
Followed by Problem 19 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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