What is the scale factor in a dilation transformation?

In a dilation transformation, the scale factor is a crucial concept that determines how much a figure is enlarged or reduced. Specifically, it is the factor by which the coordinates of the points of the original shape are multiplied to create the corresponding points of the transformed shape.

For instance, if you have a shape and you apply a dilation with a scale factor of 2, each coordinate of the shape's points will be multiplied by 2, effectively doubling the size of the shape. Conversely, if the scale factor is a fraction, such as 1/2, the shape will be reduced in size, with each coordinate being halved. This relationship illustrates how the scale factor directly affects the size and dimensions of the figure in a consistent manner without altering its shape.

Understanding the scale factor is essential for correctly applying dilation transformations in various mathematical contexts, such as geometry and coordinate transformations.