Which of the following transformations retains the geometric shape while changing its position?

The transformation that retains the geometric shape while changing its position is translation. This is because translation involves moving every point of a shape a certain distance in a specific direction without altering its size, orientation, or shape. The object essentially slides over the plane or space, maintaining all its properties, such as angles and lengths, which ensures that the original geometric shape remains intact.

In contrast, dilation alters the size of the shape, making it larger or smaller while maintaining the same proportions, but it does not simply change the position. Reflection flips the shape over a line, changing its position and orientation but not its size, while shearing distorts the shape by shifting parts of it in a given direction, which can change angles, thus altering the overall geometric integrity of the shape.