ABC is a triangle and AD is the median. If the coordinates of A are ( 4, 7,-8)and the coordinates of centroid of the triangle ABC are (1, 1, 1), then  the coordinates of D are

Let coordinates of D be $(x, y, z)$ Co-ordinates of centroid is (1, 1, 1), and of A, is ( 4, 7, 8) Centroid divides median is 2 : 1 ratio 

So, $\frac{\mathrm{AO}}{\mathrm{OD}}=2:1$

For $\mathrm{x}$ :

$\begin{array}{l}1=\frac{2\times x+1\times 4}{1+2}\\ \Rightarrow x=-1/2\end{array}$

For $\mathrm{y} :$ 

$\begin{array}{l}1=\frac{2y+1\times 7}{1+2}\\ y=-2\end{array}$

For $\mathrm{z} :$

$1=\frac{2\times \mathrm{z}+1\times -8}{3}\Rightarrow \mathrm{z}=+11/2$

$\therefore \text{ Co-ordinates of }\mathrm{D}\text{ are }(-1/2,-2,11/2)$