Difference between revisions of "2021 AMC 12A Problems/Problem 11"
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<math>\textbf{(A) }2\sqrt{10} \qquad \textbf{(B) }5\sqrt2 \qquad \textbf{(C) }10\sqrt2 \qquad \textbf{(D) }15\sqrt2 \qquad \textbf{(E) }10\sqrt5</math> | <math>\textbf{(A) }2\sqrt{10} \qquad \textbf{(B) }5\sqrt2 \qquad \textbf{(C) }10\sqrt2 \qquad \textbf{(D) }15\sqrt2 \qquad \textbf{(E) }10\sqrt5</math> | ||
| + | |||
| + | ==Diagram== | ||
| + | [[File:2021 AMC 12A Problem 11.png|center]] | ||
| + | ~MRENTHUSIASM (by Desmos: https://www.desmos.com/calculator/y6wyqok8gm) | ||
==Solution== | ==Solution== | ||
Revision as of 16:14, 14 February 2021
Contents
Problem
A laser is placed at the point 
. The laser bean travels in a straight line. Larry wants the beam to hit and bounce off the 
-axis, then hit and bounce off the 
-axis, then hit the point 
. What is the total distance the beam will travel along this path?
Diagram
~MRENTHUSIASM (by Desmos: https://www.desmos.com/calculator/y6wyqok8gm)
Solution
Every time the laser bounces off a wall, instead we can imagine it going straight by reflecting it about the wall. Thus, the laser starts at 
and ends at 
, so the path's length is 
~JHawk0224
Video Solution by OmegaLearn (Using Reflections and Distance Formula)
~ pi_is_3.14
Video Solution by Hawk Math
https://www.youtube.com/watch?v=AjQARBvdZ20
See also
| 2021 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 10 |
Followed by Problem 12 |
| 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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
