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To find the scale factor, identify the coordinates of the vertices of one pair of corresponding sides in the figures.
Dilation: Reduction
Scale Factor: 13
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.
We can tell that the image B is smaller than the original figure A. Therefore, the dilation is a reduction.
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), ( - 6,0) | sqrt(( - 6- 0)^2+( 0- 0)^2) | 6 |
B | ( 0,0), ( - 2,0) | sqrt(( - 2- 0)^2+( 0- 0)^2) | 2 |
The distance between the vertices of A is 6, and between the vertices of B the length is 2. Finally, we can find the scale factor. 2/6=1/3 The scale factor of our dilation is 13.