Three Dimensional Geometry Question 318
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?
Options:
A) $ ( -\frac{1}{2},2,11 ) $
B) $ ( -\frac{1}{2},-2,\frac{11}{2} ) $
C) $ (-1,2,11) $
D) $ (-5,-11,19) $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Let coordinated of D be (x, y, z) Co-ordinated 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=-1/2 $ For $ y:1=\frac{2y+1\times 7}{1+2} $
$ \Rightarrow y=-2 $ For $ z:1=\frac{2\times z+1\times -8}{3}\Rightarrow z=+11/2 $
$ \therefore $ Co-ordinates of D are (-1/2, -2, 11/2)
BETA
