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

Let’s consider AD be the median through A.

As we know that, AD is the median and D is the mid-point of BC

Therefore, the coordinates of D are $(1+5/2,-1+1/2)=(3,0)$

So,

Length of median $AD=\sqrt{\left[ {{(3+1)}^{2}}+{{(0-3)}^{2}} \right]}$

$=\sqrt{\left[ {{\left( 4 \right)}^{2}}+{{(-3)}^{2}} \right]}$

$=\sqrt{(16+9)}$

$=\sqrt{25}$

$=5$ units