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)

$\left(- \frac{1}{2}, -2 ,\frac{11}{2} \right)$

Answer 2

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)