For this question we will use the following formula to compute the distance between two given points (x,y) and (v,w):
[tex]d_{(x,y),(v,w)}=\sqrt[]{(x-v)^2+(y-w)^2}.[/tex]
Now, the length of segment MN is the distance between M(0,4) and N(3,-2):
[tex]\begin{gathered} d_{(3,-2),(0,4)}=\sqrt[]{(3-0)^2+(-2-4)^2}=\sqrt[]{3^2+6^2} \\ =\sqrt[]{9+36}=\sqrt[]{45}=3\sqrt[]{5}. \end{gathered}[/tex]
Answer: The length of MN is:
[tex]3\sqrt[]{5}.[/tex]
