2020 AMC 10A Problems/Problem 23
Problem
Let 
be the triangle in the coordinate plane with vertices 
and 
Consider the following five isometries (rigid transformations) of the plane: rotations of 
and 
counterclockwise around the origin, reflection across the 
-axis, and reflection across the 
-axis. How many of the 
sequences of three of these transformations (not necessarily distinct) will return to its original position? (For example, a 
rotation, followed by a reflection across the -axis, followed by a reflection across the -axis will return to its original position, but a 
rotation, followed by a reflection across the -axis, followed by another reflection across the -axis will not return to its original position.)
Solution
First, any combination of motions we can make must preserve the chirality (how many times it has been flipped) of .
See Also
| 2020 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 22 |
Followed by Problem 24 | |
| 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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