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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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When a figure slides from one position to another?
Translation.
What figure is formed by a translation of another figure?
The same figure. A translation simply moves the figure somewhere else, without changing its shape or size.
How can you tell when one figure is a reflection of another figure?
When you exchange the x and y values it creates a reflection.
What is a transformation that slides a figure horizontally and vertically called?
A transformation that slides a figure horizontally is called a translation. A transformation that slides a figure vertically is also called a translation.
What is a figure that is not changed by a horizontal reflection or a translation?
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.
