A dilation is a transformation in geometry in which a mathematical object (figure) is expanded or compressed (made larger or smaller) in such a way that the image is similar to the original.

A dilation is determined by a dilation centre and a scale factor. Every location on the image is determined by multiplying the distance from the corresponding location on the object to the dilation centre by the scale factor.

When the absolute value of the scale factor is greater than one, an expansion occurs.

When the absolute value of the scale factor is less than one, a compression occurs.

Notice that the image is similar to the object (a rectangle) but is twice as long and twice as wide. Since the scale factor is greater than one, an expansion occurs.

As stated in the definition, "every location on the image is determined by multiplying the distance from the corresponding location on the object to the centre location by the scale factor".

Note that it is easier to work with horizontal and vertical distances than distances along oblique lines.

If the dilation centre is at the origin (in a coordinate plane), multiply each value of an ordered pair associated with the object by the scale factor to obtain the coordinates of the corresponding location in the image.