Explain the enlargement, reduction, or a congruence transformationby the help of scale factor.
Explanation of Solution
Given:
The given statement is that the enlargement transformation.
Calculation:
A dilation with a scale factor greater than one produces an enlargement, or an image that is larger than the original figure.
If
Where
Example
The dilation is an enlargement because
From the diagram, for the original figure
The distance between the vertices at
For the image figure
The distance between the vertices at
Scale factor
Hence the dilation is an enlargement and Scale factor is
A dilation with a scale factor between zero and one produces a reduction, an image that is smaller than the original figure.
If
Where
Example
The dilation is a reduction because
From the diagram, for the original figure
The distance between the vertices at
For the image figure
The distance between the vertices at
Scale factor
Hence the dilation is a reduction and Scale factor is
Two objects are congruent if they have the same size and shape. In a congruence transformation, an object transformed into a congruent object. Scale factor of the congruence transformationis
Example
From the diagram, for the original figure
The distance between the vertices at
For the image figure
The distance between the vertices at
Scale factor
Hence the dilation is a congruence transformation and Scale factor is
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- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning