Difference between revisions of "2002 AMC 12B Problems/Problem 18"
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Revision as of 15:56, 2 July 2019
Contents
Problem
A point 
is randomly selected from the rectangular region with vertices 
. What is the probability that is closer to the origin than it is to the point 
?
Solution
Solution 1
The region containing the points closer to 
than to is bounded by the perpendicular bisector of the segment with endpoints 
. The perpendicular bisector passes through midpoint of , which is 
, the center of the unit square with coordinates 
. Thus, it cuts the unit square into two equal halves of area 
. The total area of the rectangle is 
, so the area closer to the origin than to and in the rectangle is 
. The probability is 
.
See also
| 2002 AMC 12B (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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
