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

Step-by-step 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=}(√((7.5-0)^2+(5-10)^2))/(√((3-0)^2+(2-4)^2))=(5)/(2)=2.5`

Therefore, the scale factor is 2.5