Dilations

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. It is defined by a center of dilation and a scale factor.

The center of dilation is a fixed point in the plane about which all points are expanded or contracted during a dilation.

The scale factor (k) is a number that describes how much a figure is enlarged or reduced during a dilation. If k > 1, the figure is enlarged; if 0 < k < 1, the figure is reduced.

The new coordinates are (8, 12).

The new coordinates are (1, 1.5).

False. A dilation produces a similar figure, not a congruent figure.

The distances between points are multiplied by the scale factor.

The figure remains unchanged.

A negative scale factor reflects the figure across the center of dilation and changes its size.

The scale factor (k) can be found by dividing the distance from the center of dilation to the dilated point by the distance from the center of dilation to the original point.