Question

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), what are the coordinates of D?

• A. $\left(-\frac{1}{2},2,11\right)$
• B. $\left(-\frac{1}{2},-2,\frac{11}{2}\right)$
• C. (-1, 2, 11)
• D. (-5, -11, 19)

Answer 1

Answer: (B)

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, $\frac{AO}{OD}=2:1$
For x :
$1=\frac{2\times x+1\times 4}{1+2}$
$\Rightarrow x=-12$
For y :
$1=\frac{2y+1\times 7}{1+2}$
$y=-2$
$1=\frac{2\times z+1\times -8}{3}\Rightarrow z=+11/2$
$\therefore$ Co-ordinates of D are (-1/2, -2, 11/2)