Which transformation involves moving a shape a fixed distance in a specified direction?

The transformation that involves moving a shape a fixed distance in a specified direction is translation. In a translation, each point of the shape moves the same distance in the same direction, effectively creating a "sliding" effect. This means that the shape maintains its size, orientation, and shape throughout the movement; only its position changes.

For instance, if you have a triangle and you translate it 3 units to the right and 2 units up, every point of the triangle will move exactly that distance in the specified direction. This transformation can be represented mathematically by adding a vector to each point's coordinates.

Understanding translations is fundamental in geometry because they can be combined with other transformations (like reflections or rotations) to create more complex movements.