In the diagram, A ABC-A DEF by the dilation with center and a scale factor of r. Explain why A DEF-A ABC.

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Dilations are enlargements

(or reductions)!!

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size.

• A dilation that creates a larger image is called an enlargement.

• A dilation that creates a smaller image is called a reduction.

• A dilation stretches or shrinks the original figure.

dipic1

• A description of a dilation includes the scale factor (or ratio) and the center of the dilation.

• The center of dilation is a fixed point in the plane.

• If the scale factor is greater than 1, the image is an enlargement (a stretch).

• If the scale factor is between 0 and 1, the image is a reduction (a shrink).

• If the scale factor is 1, the figure and the image are congruent

Step-by-step explanation:

Starting with ΔABC, draw the dilation image of the triangle with a center at the origin and a scale factor of two.

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

Dilations involve multiplication!

Dilation with scale factor 2, multiply by 2.

(x, y) → (2x,2y)

bullet Dilation scale factor ½:

  dilX2

Starting with quadrilateral ABCD (blue), draw the dilation

Explanation: