Question

What is the scale factor of the dilation of triangle DEF?

Answer 1

Answer:
`(3)/(10)`

Explanation:

Since, In the dilation of a figure, we found a transformed figure which is similar to the figure.

Also, the factor of dilation is the common ratio of the corresponding sides of the transformed figure and the figure.

Here the triangle DEF is dilated into the triangle D'E'F'

Where DE is corresponding to D'E'.

Hence,

`\text{The scale factor of dilation} = (D'E')/(DE)`

`\implies\text{ The scale factor of dilation} = (3)/(10)`

⇒ First option is correct.

Answer 2

Answer: First option 3/10

Solution

The scale factor of dilation of triangle DEF is the ratio between the corresponding sides of the triangle D'E'F' and the triangle DEF:

Scale factor: f=D'F'/DF=D'E'/DE=E'F'/EF (1)

We can find the ratio D'F'/DF using the similar triangles OD'F' and ODF, because their sides must be proportionals:

D'F'/DF=OF'/OF=OD'/OD (2)

We know according with the figure:

OF'=3 and F'F=7, then:

OF=OF'+F'F→OF=3+7→OF=10

Then replacing in (2):

(2) D'F'/DF=3/10=OD'/OD

And replacing in (1):

(1) f=3/10=D'E'/DE=E'F'/EF

Answer: The scale factor of dilation of triangle DEF is 3/10