Question

Triangle LMN has the vertices shown on the coordinate grid

Answer 1

For this question we will use the following formula to compute the distance between two given points (x,y) and (v,w):

`d_((x,y),(v,w))=\sqrt[]{(x-v)^2+(y-w)^2}.`

Now, the length of segment MN is the distance between M(0,4) and N(3,-2):

`\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}`

Answer: The length of MN is:

`3\sqrt[]{5}.`