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MATHEMATICS OBJECTIVE
Students will be able to:
Verify the properties of a dilation.
Graph the image of a dilation given a fixed center and a common scale factor.
ESSENTIAL UNDERSTANDING
After the dilation of a figure, the preimage and its image are the same shape and orientation, but different sizes. A scale factor greater than 1 produces an enlargement. A scale factor between 0 and 1 produces a reduction.
I can understand and perform dilations.
UNDERSTANDING DILATIONS
A dilation is a transformation that results in an image with the same shape,
angle measures, and orientation as the preimage, but different side lengths.
ENLARGEMENT
When the scale factor is greater than 1, the dilation is an enlargement.
Diagram: On a coordinate grid, a small blue rectangle ABCD is enlarged to a
larger orange rectangle A'B'C'D'. The orange figure is twice as wide and
twice as tall as the blue figure (scale factor 2 about the origin).
REDUCTION
When the scale factor is between 0 and 1, the dilation is a reduction.
Diagram: On a coordinate grid, a large blue square ABCD is reduced to a
smaller orange square A'B'C'D'. The image's side length is one-fourth that
of the original (scale factor 1/4 about the origin).
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