A) \[\left( -\frac{1}{2},\,\,2,\,\,11 \right)\]
B) \[\left( -\frac{1}{2},-2,\frac{11}{2} \right)\]
C) \[(-1,2,11)\]
D) \[(-5,-11,19)\]
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) |
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