A) \[(1,5)\]
B) \[\left( 1,-\frac{11}{3} \right)\]
C) \[(1,-\,3)\]
D) \[(1,6)\]
Correct Answer: B
Solution :
We know that centroid divides the orthocentre and circumcentre in the ratio \[2:1\]. |
\[G=\left( \frac{-\frac{2}{3}+\frac{11}{3}}{3},\frac{\frac{4}{3}+\frac{4}{3}}{3} \right)\] |
\[G=\left( 1,\frac{8}{9} \right)\] |
Also, \[AG:GD=2:1\] |
\[1=\frac{2h+1}{3},\frac{8}{9}=\frac{2k+10}{3}\] |
\[h=1,\]\[k=-\frac{11}{3}\] |
\[\therefore \]Coordinate of mid-point of opposite side of A is \[\left( 1,-\frac{11}{3} \right)\] |
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