Answer:
[tex]DF = 4[/tex]
Step-by-step explanation:
See attachment for proper question
From the attachment, triangle DEF is an image of ABC
By comparing the position of the angles, the following sides are similar
AB to DE
AC to DF
BC to EF
By dividing the similar sides, we calculate the scale of dilation.
[tex]Scale = \frac{DE}{AB}[/tex]
[tex]Scale = \frac{8}{4}[/tex]
[tex]Scale = 2[/tex]
To calculate DF, we make use of sides AC and DF as comparison:
[tex]Scale = \frac{DF}{AC}[/tex]
Substitute 2 for Scale and 2 for AC
[tex]2= \frac{DF}{2}[/tex]
Make DF the subject
[tex]DF = 2 * 2[/tex]
[tex]DF = 4[/tex]
