Goal:The purpose of this lesson is to illustrate how scalar multiplication yield dilations. Figures under dilation are
similar figures; all properties of the similarity chapter apply to these objects.
Vocabulary!Scale factors of the same value, such asS 2 , are also called size changes. All properties of similar figures
hold for size changes.
Extension! Scalar multiplication can be extended to multiplying thex−values andy−values by different values,
yielding a non-similar figure. For example, you could multiply the points( 0 , 2 ),( 1 , 7 ),( 4 , 5 ),( 6 , 2 )byS 2 , 3. The first
value in the subscript is the multiplier for thex−values and the second value in the subscript is the multiplier for the
y−values. The resulting ordered pairs are( 0 , 6 ),( 2 , 21 ),( 8 , 15 ),and( 12 , 6 ).
Technology!To find the image points of a size change, input a 2×2 matrix in matrix[A], such as
[
2 0
0 2
]
. For a scale
change, a matrix could look like this:
[
2 0
0 3
]
. Multiply the two matrices using the process found inReflections
lesson.
Additional Example:
a. Suppose the image JAR has the following matrix:[
2 −4 8
6 −3 5
]
, occurring under a size changeS 12. What are
the coordinates of the preimage TIP?1.12. Transformations