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Elsie is making a quilt using quilt blocks like the one in the diagram.
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is it 8 or 4 lines of symmetry?
I think there are four lines of symmetry (y=0, y=x, x=0, y =-x) through the center. Only rotations of 90 degrees or multiples there off will be equivalent.
I'm not sure how you define line of symmetry. If it reflection through the line that gives the same shape in the same position its 4, if its a reflection through one of the outer lines of the square, then the shape will look the same but be in a new position. So we need to see the exact definition. Normally when dealing a function and we talk about lines of symmetry we are talking about the first kind.