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

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:

$\frac{OQ'}{OQ}=\frac{17.1}{9.4}$

$\frac{OQ'}{OQ}=1.8191$

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

$\frac{OQ'}{OQ}\times OQ=1.8191\times OQ$

$OQ'=1.8191\times OQ$

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

$OQ'\approx 1.82\times OQ$

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