Question

Use lengths |OQ| = 9.4 units and |OQ’| = 17.1 units to determine the scale factor r of dilation D (round to the nearest hundredths place if necessary).

Show and/or explain your work. Let D be the dilation with center O and scale factor r > 0 so that dilation (P) = P’ and dilation (Q) = Q’.

Answer 1

Scale factor = 1.82 units.

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:

`(OQ')/(OQ)=(17.1)/(9.4)`

`(OQ')/(OQ)=1.8191`

Upon multiplying both sides of our equation by OQ we will get,

`(OQ')/(OQ)* OQ=1.8191* OQ`

`OQ'=1.8191* OQ`

Upon rounding our answer to nearest hundredths place we will get,

`OQ'\approx 1.82* OQ`

Since side length OQ' is 1.82 times side length OQ, therefore, our scale factor (r) will be 1.82 units.