DILATIONS

A dilation is a transformation that alters the size of a figure but not its shape, using a center point and a scale factor.

The scale factor is a number that describes how much a figure is enlarged or reduced during a dilation. It is calculated as $$\frac{new}{old}$$ .

The figure is enlarged.

The figure is reduced.

The algebraic representation is (x, y) --> (2x, 2y).

Multiply the original coordinates by the scale factor. For example, if the original point is (x, y) and the scale factor is k, the new coordinates are (kx, ky).

The scale factor can be calculated using the formula $$\frac{length\text{ of } figure A}{length\text{ of } figure B}$$ .

Two figures are similar if they have the same shape but different sizes, which means their corresponding angles are equal and their corresponding sides are proportional.

Multiply the coordinates by the scale factor: (4, 3) --> (4*3, 3*3) = (12, 9).

A negative scale factor not only changes the size of the figure but also reflects it across the center of dilation.