Certainly! Let's solve the problem step-by-step.
1. Understanding the Dilation:
- Dilation is a transformation that produces an image that is the same shape as the original, but is a different size.
- The scale factor tells us how much the figure is enlarged or reduced.
2. Given Information:
- The original measurement of line segment [tex]\(\overline{FD}\)[/tex] is 12 units.
- The scale factor of the dilation is 4.
3. Effect of Dilation:
- In a dilation, every length on the pre-image is scaled by the scale factor to produce the image.
- If a shape is dilated by a scale factor of [tex]\(k\)[/tex], the lengths of the corresponding sides in the image are multiplied by [tex]\(k\)[/tex].
4. Finding the Length of [tex]\(\overline{EF}\)[/tex]:
- Here, the original length of [tex]\(\overline{FD}\)[/tex] is given as 12 units.
- The scale factor is 4.
- However, since [tex]\(\overline{FD}\)[/tex] is already the original length, to find [tex]\(\overline{EF}\)[/tex], we need to divide by the scale factor 4:
[tex]\[
\overline{EF} = \frac{\overline{FD}}{\text{scale factor}} = \frac{12}{4} = 3 \text{ units}
\][/tex]
So, the length of [tex]\(\overline{EF}\)[/tex] is 3 units.
The correct answer is not among the options provided (6 units, 9 units, 12 units, or 16 units).
The length of [tex]\(\overline{EF}\)[/tex] should be 3 units.
