2020 AIME II Problems/Problem 2
Contents
[hide]Problem
Let be a point chosen uniformly at random in the interior of the unit square with vertices at , and . The probability that the slope of the line determined by and the point is greater than can be written as , where and are relatively prime positive integers. Find .
Solution
The areas bounded by the unit square and alternately bounded by the lines through that are vertical or have a slope of show where can be placed to satisfy the condition. One of the areas is a trapezoid with bases and and height . The other area is a trapezoid with bases and and height . Then, ~mn28407
Video Solution
https://youtu.be/x0QznvXcwHY?t=190
~IceMatrix
See Also
2020 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.