If `A(5,-1),B(-3,-2)a n d(-1,8)` are the vertices of triangle ABC, find the length of median through A and the coordinates of the centroid.

Explanation

`A D` is the median of the `triangle A B C`

`D` is the mid-point of `B C`

Mid-point of a line `=(frac{x_{1}+x_{2}}{2}, frac{y_{1}+y_{2}}{2})`

Mid-point of `B C=(frac{1+5}{2}, frac{-1+1}{2})`

`=(frac{6}{2}, frac{0}{2})`

`=(3,0)`

Length of the median `A D=sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}` `=sqrt{(3+1)^{2}+(0-3)^{2}}`

`=sqrt{4^{2}+(-3)^{2}}`

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