2019 AMC 8 Problem 6
Attempt Problem 6 of the 2019 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2019 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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?
Answer: C
Small hint:
A square has symmetry lines
Big hint:
Each symmetry line has possible points besides
Video solution:
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Written solution:
Note the only lines of symmetry for a square are the two diagonals and the two lines connecting opposite midpoints.
On each symmetry line there are grid points other than The four lines intersect only at which is not eligible, so these give distinct choices for
The probability is therefore
Thus, the correct answer is C.
Problem 6 in other years
- 1985 AMC 8
- 1986 AMC 8
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