Explain what dilation is in geometry.

In geometry, dilation is a transformation that changes the size of a geometric figure without changing its shape. It involves scaling a figure up or down by a factor called the scale factor, while keeping the orientation and proportions of the figure the same.

To perform a dilation, we choose a fixed point called the center of dilation and a scale factor which determines by how much the figure will be enlarged or reduced. Then, for each point in the original figure, we draw a line connecting the point to the center of dilation, and then extend it to a point that is the appropriate distance away from the center of dilation, as determined by the scale factor. The resulting figure is a dilated version of the original figure, which has the same shape but is either larger or smaller than the original.

Dilations are used in many areas of geometry, such as to create similar figures, to find the image of a figure under a transformation, and to measure the similarity or congruence of two figures. Dilations can also be used in real-life situations, such as in maps or blueprints, where objects need to be scaled up or down to fit on a page or in a particular space.