Question

A(5 1) b(1 5) and c(-3 -1) are the vertices of triangle abc. find the LENGTH of median ad

Answer 1

Answer:

$\text{Length of median AD}=\sqrt{37}$

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

$\text{Mid Point :}\left ( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2} \right )$

D is mid point of B(1,5) and C(-3,-1)

$\therefore D \left ( \frac{1-3}{2},\frac{5-1}{2} \right )\Rightarrow (-1,2)$

AD is median of triangle ABC. Now we find length of median AD using distance formula of two coordinate.

$\text{Distance }=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

A(5,1) and D(-1,2)

$AD=\sqrt{(5+1)^2+(1-2)^2}\Rightarrow \sqrt{36+1}$

$\text{Length of median AD}=\sqrt{37}$

Thus, $\text{Length of median AD}=\sqrt{37}$