notes dilations. definitions dilation - a transformation in which every point p has an image p'...
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Notes Dilations
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DefinitionsDilation - a transformation in which every point P
has an image P' placed on OP so that
and OP' = k * OP
Center of Dilation – the point from which an original figure is dilated.
Scale Factor - the ratio of the image length to the corresponding original length.
'OPk
OP
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Scale Factor• If the scaled factor is greater than 1, then it
is an enlargement (k>1).
• If the scaled factor is equal to 1, then it is a congruent figure (k=1)
• If the scale factor is less than 1, then it is a reduction (k<1).
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Corresponding distances
42
= = 2Image Distance
Original Distance= k
Scale Factor
2 > 1
This dilation is an enlargement .
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Corresponding distances
23
= Image Distance
Original Distance= k
Scale Factor
2/3 < 1
This dilation is an reduction.
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Example:1. Rectangle W’X’Y’Z’
is the image of rectangle WXYZ after a dilation.
a. Find the scale factor of the dilation.
b. Tell whether the image is a reduction or an enlargement.
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Example:2.
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Example:3.
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Reduction, Enlargement, or Congruent?
1. K = 4
2. K = ½
3. K = 1
4>1 Enlargement
½ <1 Reduction
Congruent
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MatchingA. K = ¼
B. K = 3
C. K = 2/7
D. K = 1
E. K = 5
F. K = 3/8
Reduction
Enlargement
Congruent
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7. scale factor 2
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8. scale factor ¼
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8. scale factor 1/3