Answer:
A, D , and E
Step-by-step explanation:
We have that:
[tex]\overline{CD} = 12 \: units[/tex]
[tex]\overline{C'D'}[/tex]
is the image of CD after a dilation of scale factor n.
We use the relation between the image length and object length:
[tex]\overline{C'D'} = n \times \overline{CD}[/tex]
Option A
If n=3/2, then
[tex]\overline{C'D'} = \frac{3}{2} \times 12 = 3 \times 6 = 18 \: units[/tex]
This is true.
Option B
If n=4, then
[tex] \overline{C'D'} = 4 \times 12 = 36 \: units[/tex]
This is false.
Option C
If n=8, then
[tex] \overline{C'D'} = 8 \times 12 = 96 \: units[/tex]
This too is false.
Option D
If n=2, then
[tex]\overline{C'D'} = 2 \times 12 = 24 \: units[/tex]
This is true
Option E
If n=3/4, then
[tex]\overline{C'D'} = \frac{3}{4} \times 12[/tex]
[tex]\overline{C'D'} = 3 \times 3 = 9 \: units[/tex]
This is also true.
