To find the length of [tex]\(\overline{DE}\)[/tex], given that the triangle was dilated by a scale factor of 2 and [tex]\(\overline{FD}\)[/tex] measures 6 units, you need to apply the property of dilation.
When a geometric figure is dilated by a scale factor, all lengths in the figure are multiplied by that scale factor.
Here’s a step-by-step explanation:
1. The original length of [tex]\(\overline{FD}\)[/tex] is given as 6 units.
2. The dilation process increases all lengths in the figure by the scale factor.
In this problem, the scale factor is 2.
3. To find the new length of [tex]\(\overline{DE}\)[/tex], multiply the original length [tex]\(\overline{FD}\)[/tex] by the scale factor:
[tex]\[
\overline{DE} = \overline{FD} \times \text{scale factor}
\][/tex]
4. Substituting the given values:
[tex]\[
\overline{DE} = 6 \, \text{units} \times 2
\][/tex]
5. This calculation gives:
[tex]\[
\overline{DE} = 12 \, \text{units}
\][/tex]
Therefore, the length of [tex]\(\overline{DE}\)[/tex] is [tex]\(12\)[/tex] units. The correct answer is:
[tex]\[
\boxed{\overline{DE}=12}
\][/tex]
