What is a dilation?

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. A dilation can be an enlargement (making the figure bigger) or a reduction (making the figure smaller).

Here are the key aspects of a dilation:

• Scale Factor: This is the ratio of the new image size to the original image size. If the scale factor is greater than 1, the dilation is an enlargement. If the scale factor is between 0 and 1, the dilation is a reduction. If the scale factor is 1, then the figure doesn't change.

• Center of Dilation: This is a fixed point in the plane about which the dilation is performed. All points of the original figure are scaled away from (or towards) this center.

• The orientation of the image remains the same after a dilation. The image is similar to the original but not congruent (unless the Scale Factor is 1).

• To dilate a figure, you multiply the coordinates of each point on the figure by the Scale Factor centered at the origin (0,0). If the center is not the origin, a translation is required before and after the scaling.