In what type of transformation do points retain their shape but change position?

The choice of translation as the correct answer is appropriate because a translation is a type of transformation that shifts every point of a figure or a shape by the same distance in a specified direction. This means that while the position of the points changes, their relative arrangement, angles, and the overall shape of the figure remain unchanged.

In a translation, you can think of it as moving the entire figure along a straight path on a coordinate plane without altering its characteristics. For example, if you have a triangle, translating it means moving the triangle to a new location where the shape and size of the triangle remain the same, but its position changes.

In contrast, other transformations such as reflection involve flipping the figure over a line, rotation involves turning the figure around a point, and dilation involves resizing the figure while maintaining its shape. These transformations either alter the orientation or size of the shape rather than simply changing its position. Therefore, translation is distinctly characterized by its ability to maintain the original shape of the figure while changing its location.