reminder
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.
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• 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 image of the quadrilateral with a center at the origin and a scale factor of ½.
Each vertex of ABCD is multiplied by ½.
Dilation with scale factor ½, multiply by ½.
(x, y) → (½x, ½y )
In this problem, the center of the dilation is NOT at the origin.
bullet Dilation not at origin:
dilX3
Starting with rectangle ABCD (green), draw the dilation image of the rectangle with the center of dilation at point A and a scale factor of 1/3
Notice that point A and its image are the same.
You must observe the distances from the center of the dilation at point A to the other points B, C and D. The dilation image will be 1/3 of each of these distances.
AB = 6, so A'B' = 2.
AD = 9, so A'D' = 3. Now, draw the image rectangle.
FYI:
dilmathHyp
For a dilation not at the origin,
measure the distances.
Dilations and Similarity:
The term similar (or similarity) can be defined using the language of transformations.
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Two figures are similar if one is the image of the other under a transformation from the plane into itself that multiplies all distances by the same positive scale factor. That is to say, one figure is a dilation of the other.
dil Sim M
