Before we begin, recall that a dilation is a transformation that enlarges or reduces the original figure proportionally. There are two types of dilation.
Enlargement: The image is larger than the original figure and is produced by a scale factor greater than 1.
Reduction: The image is smaller than the original figure and is produced by a scale factor less than 1.
We will determine the given dilation first. Then we can find the scale factor.
Dilation
Let's analyze the given dilation.
We can tell that the image B is bigger than the original figure A. Therefore, the dilation is an enlargement.
Scale Factor
The scale factor is the ratio of a length on image A to a corresponding length on the preimage B. Before we find the scale factor, let's identify the coordinates of the vertices of one pair of corresponding sides in our figures.
Now we can find the length of these sides using the Distance Formula.
Figure
Vertices
Distance Formula
Simplified
A
( 0,1), ( 0,3)
sqrt(( 0- 0)^2+( 3- 1)^2)
2
B
( 3,1), ( 3,5)
sqrt(( 3- 3)^2+( 5- 1)^2)
4
The distance between the vertices of A is 2, and between the vertices of B the length is 4. Finally, we can find the scale factor.
4/2=2
The scale factor of our dilation is 2.
