What type of transformation is described by moving a figure across a graph without altering its shape or size?

The transformation that involves moving a figure across a graph without changing its shape or size is known as a translation. This process shifts every point of the figure a certain distance in a specified direction. For instance, if you are translating a triangle, each vertex of the triangle will move the same distance and direction, ensuring that the triangle retains its original shape and size.

In contrast, other types of transformations have different effects: reflection involves flipping a figure over a specific line, creating a mirror image; rotation involves turning a figure around a fixed point, changing its orientation but not its size; and dilation alters the size of the figure while maintaining its shape, either enlarging or reducing it. Therefore, among the given choices, translation is the only transformation that strictly adheres to moving a figure without any alterations to its shape or size.