¶ Spring 2021 AMC 12A Problem 11
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?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Reflect about the -axis to get . Reflecting this point about the -axis gives . Because reflection is an isometry and the angle of incidence equals the angle of reflection, the segment of the beam's travel from to has the same length as the line segment from to , and the segment of the beam's travel from to has the same length as the line segment from to . Therefore the total distance of the path from to is equal to the distance
The problems on this page are the property of the MAA's American Mathematics Competitions