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Dilations are the fourth and final transformation. Dilations involve shrinking or enlarging a figure using a scale factor. Think about going to the eye doctor to have your eyes dilated. They put drops in your eyes that cause the pupil to get bigger. When you go in the sun, the pupil shrinks. These are dilations. Dilations change the size, but not the shape of an object. They are unique in that they create similar figures (not congruent like the other transformations). Similar figures are those that have the same angle measurements, but the corresponding side lengths are proportional. Another way to know if two figures are similar rather than congruent is if they are the same SHAPE but not the same SIZE. The scale factor tells you how much bigger or smaller the object is after the dilation. A scale factor greater than one will enlarge a figure. A scale factor less than is a fraction less than one will shrink the figure. Just like in rotations, we have to know where the center of dilation is located. For our purposes, we will stick to the center of dilation being the origin (0,0). If the center of dilation is the origin, you can multiply both the x and y coordinate by the scale factor to get the new coordinates after the dilation. The important thing to remember is that dilations create SIMILAR figures.
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