Question

segment DF is dilated from the origin to create segment D prime F prime at D′ (0, 10) and F′ (7.5, 5).What scale factor was segment DF dilated by?

Answer 1

Explanation

For the initial points (The pre-image )

$\begin{gathered} D=(0,4) \\ F=(3,2) \end{gathered}$

And the image

$\begin{gathered} D^{\prime}=(0,10) \\ F^{\prime}=(7.5,5) \end{gathered}$

The scale factor will be obtained by finding the ratio of the distance between D'F' and DF

$scale\text{ factor=}\frac{\sqrt{(7.5-0)^2+(5-10)^2}}{\sqrt{(3-0)^2+(2-4)^2}}=\frac{5}{2}=2.5$

Therefore, the scale factor is 2.5