Which geometric operation results in maintaining the original appearance of figures?

The operation that maintains the original appearance of figures is rotation around the center of the figure. When a figure is rotated about its center, all points of the figure move in a circular path around the center, but the shape and size remain unchanged. This means that the original dimensions, angles, and proportions are preserved, and the figure appears exactly the same after the rotation as it did before.

Considering the other options helps understand why they do not fit this criterion as directly as rotation. Scaling alters the size of the figure, which changes its appearance, and unless it's a uniform scaling of 1, the figure does not remain the same in terms of dimensions. Reflection across any plane can change the orientation, effectively flipping the figure and potentially giving it a mirrored appearance that is not the same as the original. Translation, while it does move the figure without altering its size or shape, can change the figure's position in space, meaning it does not maintain the original placement or context, even though the appearance remains unchanged.

Thus, rotation around the center of the figure is the operation that best describes a transformation that keeps the original appearance intact.