# Dilation (Geometry)

How to solve dilation problems: formula, examples, and their solutions.

## Formula

The image of a point (*x*, *y*),

whose image is under the dilation of *k*,

is (*kx*, *ky*).

Multiply the scale factor *k* on the coordinates.

## Example 1

Dilation of 2:

(*x*, *y*) → (2⋅*x*, 2⋅*y*)

If | *k* | > 1,

then the image is enlarged.

## Example 2

Dilation of 1/3:

(*x*, *y*) → ([1/3]⋅*x*, [1/3]⋅*y*)

If 0 < | *k* | < 1,

then the image is reduced.

If *k* = -1,

then the image shows the reflection in the origin:

(*x*, *y*) → ([-1]⋅*x*, [-1]⋅*y*) = (-*x*, -*y*).