Answer:
Scale factor = 1.82 units.
Step-by-step explanation:
We have been given that side length OQ of our prei-mage is 9.4 units and side length OQ' after dilation is 17.1 units. Since our pre-image (original image) is smaller than our new image, so our scale factor (r) will be greater than 1.
Since we know that in a dilation, the sides of the pre-image and the corresponding sides of the image are proportional, so we will use proportion to find a scale factor our given side lengths as:
[tex]\frac{OQ'}{OQ}=\frac{17.1}{9.4}[/tex]
[tex]\frac{OQ'}{OQ}=1.8191[/tex]
Upon multiplying both sides of our equation by OQ we will get,
[tex]\frac{OQ'}{OQ}\times OQ=1.8191\times OQ[/tex]
[tex]OQ'=1.8191\times OQ[/tex]
Upon rounding our answer to nearest hundredths place we will get,
[tex]OQ'\approx 1.82\times OQ[/tex]
Since side length OQ' is 1.82 times side length OQ, therefore, our scale factor (r) will be 1.82 units.
