Here is a trapezoid on a coordinate grid with the origin (0, 0) as the center of dilation: Trapezoid with origin as center of dilationį we choose a scale factor of 2, every plotted point on the polygon will be multiplied by 2 to create the enlarged image. Let's see the scale factor at work on a coordinate plane. Scale factor of dilation Dilation examples If you multiply the original coordinates:īy whole numbers other than 1, you enlarge the preimage in producing the image.īy 1, you produce an image congruent to the preimage.īy fractions or decimals, you shrink the preimage to produce the image.īy negative numbers, you will produce an image that is the inverse (upside down) of the preimage, equidistant from the center of dilation but on the opposite side. The scale factor of a dilation is the amount by which all original terms are enlarged or shrunk, usually on a coordinate plane. Here we still have a square as the preimage, but the center of the dilation is the top-left vertex, so the dilated images (one smaller, one larger) all share that same vertex. The center of the dilation does not need to be inside the shape. Its center of dilation is its exact middle, so any dilation from the square will still be a square with all parts equidistant from the center point: Center of dilation pre-image and image

You can think of the preimage as the original figure, and the image as the new figure.

The preimage and image are similar figures. Dilation - math definitionįrom that center of dilation, the preimage – the mathematical element before scaling – is enlarged, inverted, or shrunk to form the image. This can be a single point on a coordinate grid, the middle of a polygon, or any fixed point in space.

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