**Transformations: Dilations**

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The thesaurus lists the meaning of the word **dilate** come mean"*make or end up being wider, larger, or more open*". In mathematics, a dilation transforms the dimension of a figure. The number may end up being larger or smaller, however the form of the number will not change.

The native " dilate" is frequently heard in relationship to the human being eye. "The student of the eyes were dilated." together light hits the eye, the pupil enlarges or contracts relying on the amount of light. School or holiday photo packages offer the same picture in a selection of sizes, from huge to medium to little wallet dimension photos. Russian nesting dolls room a collection of wooden dolls of to decrease size placed inside one another. After the the smallest doll, each doll is one enlargement that its within doll. The zoom attribute will enlarge or mitigate the the town hall window. Soft drink containers come in a range of sizes. If some room of different shapes, rather are just enlargements. You are watching: Which scale factor would produce a contraction under a dilation of the original image Product logos have the right to come in a selection of sizes, such as these pizza shop logos on their small, medium and big boxes. Grow toys are sponge/foam playthings that "grow" when inserted in water. Some prosper quickly, when others flourish over number of days. |

*description*that a dilation contains the scale aspect and also the facility of the dilation. The scale factor may additionally be described as the scalar factor. If the larger tiger is twice as tall as the smaller sized tiger, the scale variable is 2.

If the *scale factor* is greater than 1, the photo is an **enlargement.** If the *scale variable *is in between 0 and 1, the image is a **reduction. **

In the diagram below, *A"B"C"D"* is the image of *ABCD* under a dilation.

A figure and its dilation are similar figures. Rectangle *ABCD *(shown above) is similar to rectangle *A"B"C"D". *

The street from the facility of the dilation to every vertex allude of the photo is equal to the street from the facility of the dilation come each matching vertex allude of the original number times the range factor. The size of each side of the photo is same to the length of the equivalent side the the original figure multiplied through the scale factor.

A **dilation** is a revolution that produces photo that is the very same shape as the original, yet is a various size. The description of a dilation consists of the scale factor (constant the dilation) and the facility of the dilation. The center of a dilation is a fixed point in the plane around which every points are increased or contracted. The center is the only invariant (not changing) point under a dilation, and also may be situated inside, outside, or on a figure.

• A dilation the creates a larger picture is called an • A dilation is |

• A summary of a dilation consists of the scale factor (or ratio) and also the facility of the dilation. • The

*center the dilation*is a fixed point in the plane. • If the scale element is higher than 1, the photo is one enlargement. It expands. • If the scale variable is in between 0 and also 1, the picture is a reduction. It contracts. • If the scale factor is 1, the figure and also the image are the exact same size (congruent).

Dilations in the name: coordinates plane: most dilations in the coordinate aircraft use the origin, (0,0), together the facility of the dilation. The facility of the dilation will certainly be shown within the difficulty (or in ~ the notation).

Dilation scale variable 2:

starting with Δ*ABC*, attract the dilation picture of the triangle with a facility at the origin and also a scale variable of two.

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Notice the **every** coordinate of the original triangle has been multiply by the scale factor (x2).