Answer
12
Step-by-step explanation
The length of a segment with endpoints (x₁, y₁) and (x₂, y₂) is calculated as follows:
[tex]length=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
In this case, the endpoints are C(0,3) and D(0,7), then the length of the segment CD is:
[tex]\begin{gathered} \bar{CD}=\sqrt{(0-0)^2+(7-3)^2} \\ \bar{CD}=\sqrt{4^2} \\ \bar{CD}=4 \end{gathered}[/tex]
After CD is dilated by a factor of 3, the length of the image will be:
[tex]\begin{gathered} \text{ length of the image of CD = }3\times\text{ length of CD} \\ \text{ length of the image of CD = }3\times4 \\ \text{ length of the image of CD = 12} \end{gathered}[/tex]
