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The original figure and its image must be of the same size and the same orientation. That is, you should be able to get from the original to the image by moving the shape along the x-axis and the y-axis and nothing else.

However, if the shape has rotational or reflective symmetry, there is no way that you can be sure that it has not been rotated or reflects (as appropriate).

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Q: How do you tell if a figure is a translation of another?
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When a figure slides from one position to another?

Translation.


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No figure is changed by a translation so the last part of the question is irrelevant. Any figure with a horizontal line of symmetry will not be changed by a horizontal reflection.


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