Which transformation preserves the shape but changes the size of a figure?

Dilation is the transformation that preserves the shape of a figure while changing its size. In a dilation, a figure is expanded or contracted from a center point, known as the center of dilation, by a scale factor. If the scale factor is greater than 1, the figure increases in size; if it's between 0 and 1, the figure decreases in size.

What is unique about dilation compared to the other transformations is that while it alters the dimensions of the figure, it maintains the same proportions and angles among corresponding parts, thereby preserving the overall shape. This means that corresponding shapes after dilation remain similar, exhibiting the same shape regardless of the change in size.

In contrast, transformations such as translation, rotation, and reflection involve moving the figure or changing its orientation without altering its size or shape. Translation moves a figure horizontally or vertically, rotation pivots it around a point, and reflection flips it over a line. All these transformations keep the figure's size constant while changing its position or orientation, unlike dilation, which varies the size.