Question: Reflective symmetry over y = (3/5)x ?
Answer: No
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Question: Reflective symmetry over y = (5/3)x ?
Answer: No
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Explanation:
For any parallelogram that's a square, we'll have four lines of symmetry: The two diagonals and two extra lines of symmetry for the opposite pairs of sides.
In this case, we don't have a square (we can prove this by finding the lengths of each side of the parallelogram), so we move on.
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If the parallelogram is a rectangle, then we'll have two lines of symmetry: one for each pair of opposite sides.
However, we don't have a rectangle either. We can prove this by finding the slopes of the blue lines of the parallelogram, and finding they are not perpendicular slopes.
So we move on.
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The last case is a parallelogram that isn't a rectangle. So it's not a square either. That's what we have here. For parallelograms of this nature, there are no lines of symmetry. We cannot fold it along any line to have it match up with itself.
So that's why the answer is "no" to both of these questions.
