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2019 AMC 8 Question 6

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Re: 2019 AMC 8 Question 6
by John Lensmire - Thursday, April 9, 2020, 12:25 PM

A square has different lines of symmetry. For example, a vertical line through $P$ is one such line of symmetry (because then the square is the same to the left and to the right of the line):

Note this line contains $P$ and $4+4 = 8$ other points. Therefore, if $Q$ is one of these $8$ points, $PQ$ is a line of symmetry for the square.

With one line of symmetry done, how many other lines of symmetry do we need to consider? How many other points do they contain?