Question

If $A(-1,3),B(1,-2)$ and $C(5,1)$ are the vertices of a triangle $ABC$, find the length of the median through $A$.

Answer 1

Mid point of $(x,y)$ mid and $(x_2,y_2)$ then $x=c(5,1)$

Mid point formula

If $(x,y)$ mid point of $(x_1,y_1)$ and $(x_2,y_2)$

then x $=\frac{x_1+x_2}{2}$ , $y=\frac{y_1+y_2}{2}$

We know Median bisects :

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

$=(3,-\frac{1}{2})$

Length of Median $=\sqrt{(-1-3{)}^2+{(3+\frac{1}{2})}^2}$

$=\sqrt{16+\frac{49}{4}}$

$=\sqrt{\frac{113}{4}}$