Difference between revisions of "2019 AMC 8 Problems/Problem 6"
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− | Problem | + | == Problem 6 == |
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− | |||
− | |||
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− | + | There are <math>81</math> grid points (uniformly spaced) in the square shown in the diagram below, including the points on the edges. Point <math>P</math> is in the center of the square. Given that point <math>Q</math> is randomly chosen among the other 80 points, what is the probability that the line <math>PQ</math> is a line of symmetry for the square? | |
− | + | ||
+ | <asy> | ||
+ | draw((0,0)--(0,8)); | ||
+ | draw((0,8)--(8,8)); | ||
+ | draw((8,8)--(8,0)); | ||
+ | draw((8,0)--(0,0)); | ||
+ | dot((0,0)); | ||
+ | dot((0,1)); | ||
+ | dot((0,2)); | ||
+ | dot((0,3)); | ||
+ | dot((0,4)); | ||
+ | dot((0,5)); | ||
+ | dot((0,6)); | ||
+ | dot((0,7)); | ||
+ | dot((0,8)); | ||
+ | |||
+ | dot((1,0)); | ||
+ | dot((1,1)); | ||
+ | dot((1,2)); | ||
+ | dot((1,3)); | ||
+ | dot((1,4)); | ||
+ | dot((1,5)); | ||
+ | dot((1,6)); | ||
+ | dot((1,7)); | ||
+ | dot((1,8)); | ||
+ | |||
+ | dot((2,0)); | ||
+ | dot((2,1)); | ||
+ | dot((2,2)); | ||
+ | dot((2,3)); | ||
+ | dot((2,4)); | ||
+ | dot((2,5)); | ||
+ | dot((2,6)); | ||
+ | dot((2,7)); | ||
+ | dot((2,8)); | ||
+ | |||
+ | dot((3,0)); | ||
+ | dot((3,1)); | ||
+ | dot((3,2)); | ||
+ | dot((3,3)); | ||
+ | dot((3,4)); | ||
+ | dot((3,5)); | ||
+ | dot((3,6)); | ||
+ | dot((3,7)); | ||
+ | dot((3,8)); | ||
+ | |||
+ | dot((4,0)); | ||
+ | dot((4,1)); | ||
+ | dot((4,2)); | ||
+ | dot((4,3)); | ||
+ | dot((4,4)); | ||
+ | dot((4,5)); | ||
+ | dot((4,6)); | ||
+ | dot((4,7)); | ||
+ | dot((4,8)); | ||
+ | |||
+ | dot((5,0)); | ||
+ | dot((5,1)); | ||
+ | dot((5,2)); | ||
+ | dot((5,3)); | ||
+ | dot((5,4)); | ||
+ | dot((5,5)); | ||
+ | dot((5,6)); | ||
+ | dot((5,7)); | ||
+ | dot((5,8)); | ||
+ | |||
+ | dot((6,0)); | ||
+ | dot((6,1)); | ||
+ | dot((6,2)); | ||
+ | dot((6,3)); | ||
+ | dot((6,4)); | ||
+ | dot((6,5)); | ||
+ | dot((6,6)); | ||
+ | dot((6,7)); | ||
+ | dot((6,8)); | ||
+ | |||
+ | dot((7,0)); | ||
+ | dot((7,1)); | ||
+ | dot((7,2)); | ||
+ | dot((7,3)); | ||
+ | dot((7,4)); | ||
+ | dot((7,5)); | ||
+ | dot((7,6)); | ||
+ | dot((7,7)); | ||
+ | dot((7,8)); | ||
+ | |||
+ | dot((8,0)); | ||
+ | dot((8,1)); | ||
+ | dot((8,2)); | ||
+ | dot((8,3)); | ||
+ | dot((8,4)); | ||
+ | dot((8,5)); | ||
+ | dot((8,6)); | ||
+ | dot((8,7)); | ||
+ | dot((8,8)); | ||
+ | label("P",(4,4),NE); | ||
+ | </asy> | ||
+ | |||
+ | <math>\textbf{(A) }\frac{1}{5}\qquad\textbf{(B) }\frac{1}{4} \qquad\textbf{(C) }\frac{2}{5} \qquad\textbf{(D) }\frac{9}{20} \qquad\textbf{(E) }\frac{1}{2}</math> | ||
+ | |||
+ | ==Solution 1== | ||
+ | |||
+ | |||
+ | ==See Also== | ||
+ | {{AMC8 box|year=2019|num-b=14|num-a=16}} | ||
+ | |||
+ | {{MAA Notice}} |
Revision as of 13:59, 20 November 2019
Problem 6
There are grid points (uniformly spaced) in the square shown in the diagram below, including the points on the edges. Point is in the center of the square. Given that point is randomly chosen among the other 80 points, what is the probability that the line is a line of symmetry for the square?
Solution 1
See Also
2019 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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 AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.