6. Similarity Transformations
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Before we begin, recall that a dilation is a transformation that enlarges or reduces the original figure proportionally. There are two types of dilation.
We will determine the given dilation first. Then we can find the scale factor.
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.
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 | (0,0), (4,0) | (4−0)2+(0−0)2 | 4 |
B | (0,0), (8,0) | (8−0)2+(0−0)2 | 8 |