Difference between revisions of "2019 AMC 8 Problems/Problem 6"
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== Problem 6 == | == Problem 6 == | ||
− | 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? | + | 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 <math>80</math> points, what is the probability that the line <math>PQ</math> is a line of symmetry for the square? |
<asy> | <asy> |
Revision as of 12:01, 22 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
points, what is the probability that the line
is a line of symmetry for the square?
Solution 1
Lines of symmetry go through point P, and there are 8 directions the lines could go, and there are 4 dots at each direction. 4
8/80=
.
~heeeeeheeeeeee
See Also
2019 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 5 |
Followed by Problem 7 | |
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 |
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