Answer:
Option D is correct.
The length of segment DE = 4 unit ,
Length of segment EF = 5 unit
Length of segment DF = 2 unit
Explanation:
Given:
If Δ ABC [tex]\sim[/tex] Δ DEF and the scale factor from ABC to DEF is [tex]\frac{1}{7}[/tex]
We know that:
Scale factor=measure triangle DEF/measure triangle ABC
then,
[tex]\frac{DE}{AB} =k[/tex] , [tex]\frac{DF}{AC} =k[/tex] , and [tex]\frac{EF}{BC} =k[/tex]
Scale factor (k) = [tex]\frac{1}{7}[/tex]
From the figure; we have
length of segment AB = 28 unit
length of segment AC = 14 unit
Length of segment BC = 35 unit
Then,
* [tex]\frac{DE}{28} =\frac{1}{7}[/tex]
or
[tex]DE = \frac{1}{7} \times 28 = 4 unit[/tex]
* [tex]\frac{DF}{14} =\frac{1}{7}[/tex]
or
[tex]DF = \frac{1}{7} \times 14 = 2 unit[/tex]
* [tex]\frac{EF}{35} =\frac{1}{7}[/tex]
or
[tex]EF = \frac{1}{7} \times 35 = 5 unit[/tex]
Therefore, the length of segment DE , EF and DF are; 4 unit, 5 unit , and 2 unit.
