Triangle LMN has the vertices shown on the coordinate grid

Question

asked Nov 2, 2023 179k views

1 Answer

PJK · Answer 1 · 2023-11-07T04:21:06+0000

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:

$3\sqrt[]{5}.$