Question

$A(5,1),B(1,5)$ and $C(-3,-1)$ are the vertices of $△ABC$. Find the length of median $AD$.

Answer 1

To find the coordinate of D;-

D is the midpoint of BC

Coordinate of D$=\left(\frac{1+\left(-3\right)}{2},\frac{5+\left(-1\right)}{2}\right)$

Coordinate of D$=(-1,2)$

Now,

To find the length of AD;-

$\begin{array}{c}=\sqrt{{\left(Y_2-Y_1\right)}^2+{\left(X_2-X_1\right)}^2}\\ =\sqrt{{\left(1-2\right)}^2+\left(5-\left(-1\right)\right)}\\ =\sqrt{{\left(-1\right)}^2+{\left(6\right)}^2}\end{array}$

Hence, we get $AD$$=\sqrt{37}$