Answer:
[tex]\text{Length of median AD}=\sqrt{37}[/tex]
Step-by-step explanation:
We are given the vertices of triangle ABC. We need to find the length of median AD.
Please see the attachment for figure.
D is mid point of BC because median bisect the opposite side of triangle.
Using the formula of mid point. we get coodrinate of D
[tex]\text{Mid Point :}\left ( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} \right )[/tex]
D is mid point of B(1,5) and C(-3,-1)
[tex]\therefore D \left ( \frac{1-3}{2},\frac{5-1}{2} \right )\Rightarrow (-1,2)[/tex]
AD is median of triangle ABC. Now we find length of median AD using distance formula of two coordinate.
[tex]\text{Distance }=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
A(5,1) and D(-1,2)
[tex]AD=\sqrt{(5+1)^2+(1-2)^2}\Rightarrow \sqrt{36+1}[/tex]
[tex]\text{Length of median AD}=\sqrt{37}[/tex]
Thus, [tex]\text{Length of median AD}=\sqrt{37}[/tex]
