Dilations

Dilation – is a transformation in which a given figure is enlarged or reduced.

Scale Factor – n determines the enlargement or reduction of the preimage.

If n > 1, then this indicates an enlargement

If n < 1, then this indicates a reduction

If n = 1, then the figure stays the same

*The image of P(x, y) under a dilation in the coordinate plane with the origin as the center of dilation and a scale factor n is P'(nx, ny)

(x, y) –> (nx, ny)   – basically multiply each coordinate by the scale factor

ex: n = 3    (3, 2) —> (9, 6)

*To find the scale factor, you have to compute:

The x-coordinate of the image / the x-coordinate of the preimage

or the y-coordinate of the image / the y-coordinate of the preimage

An isometry is a transformation under which the image and preimage are congruent. Reflections, translations, and rotations are all isometries.

*A dilation is not an isometry