1. Dilatation, also known as dilation, is a transformation in geometry where a figure is enlarged or reduced from a fixed point called the center of dilation. 2. The size changes, but the shape remains the same, and all angles remain equal. 3. The scale factor determines how much the figure is enlarged or reduced. If the scale factor is greater than 1, the figure enlarges; if it is between 0 and 1, the figure reduces. 4. The formula for dilatation is: $$D_{k,C}(P) = C + k(P - C)$$ where $D_{k,C}(P)$ is the image of point $P$ after dilation, $k$ is the scale factor, and $C$ is the center. 5. This means each point $P$ moves along the line connecting it to the center $C$, scaled by the factor $k$ away from $C$. 6. Dilatations are useful in geometry to change the size of objects while preserving their shape.