A dilation is a that enlarges or reduces the size of a figure. Therefore, the created will have a different size than the . However, a dilation preserves angle measures and the ratio between corresponding parts.

Concept ### Center of dilation

The center of dilation is a point that regulates where the image of the figure is placed.

From the center of dilation, $C,$ segments are drawn through the vertices of the .

The lengths between $C$ and the vertices of the figure will then be scaled by the scale factor. This will determine if the image is placed closer or further from $C$ than the preimage. The center of dilation could also be a vertex of the figure. In that case, some of the segments drawn will only be extensions of the segments in the figure.

In a dilation, the scale factor refers to the ratio between the corresponding sides of the and the . Therefore, the scale factor,

$k,$ can be calculated by dividing the length of one part in the image with the corresponding part in the preimage. The length of the preimage part should always be in the denominator as it belongs to the original figure.

When dilating a figure, the different parts of the figure are multiplied by the scale factor.

Concept ### Enlargement and reduction

Depending on the scale factor, the image will become bigger or smaller than the preimage.
If the scale factor is greater than

$1,$ the sides of the image will be longer than the sides of the preimage. This is called an enlargement, and it will place the image further away from the center of dilation than the preimage.

As opposed to an enlargement, if the scale factor is a positive number less than

$1$ the image will have shorter sides that the preimage. This is a reduction and moves the image closer to

$C$ than the preimage.