A) (3, 6)
B) (1, 2)
C) (4, 8)
D) \[(-3,\text{ }6)\]
E) \[(-1,2)\]
Correct Answer: B
Solution :
Let \[({{x}_{1}},{{y}_{1}}),({{x}_{2}},{{y}_{2}})\]and\[({{x}_{3}},{{y}_{3}})\]are co-ordinates of the points D, E and F which divide each A3, BC and CA respectively in the ratio \[3:1\]internally \[\therefore \] \[{{x}_{1}}=\frac{3\times 6-1\times 1}{4}=\frac{17}{4}\] \[{{y}_{1}}=\frac{-2\times 3+4}{4}=-\frac{2}{4}=-\frac{1}{2}\] Similarly, \[{{x}_{2}}=0,{{y}_{2}}=\frac{5}{2}\] \[{{x}_{3}}=-\frac{5}{4},{{y}_{3}}=4\] Let\[(x,\text{ }y)\]be the co-ordinate of centroid of\[\Delta DEF\] \[x=\frac{1}{3}\left( \frac{17}{4}+0-\frac{5}{4} \right)=1\]and \[y=\left( -\frac{1}{2}+\frac{5}{2}+4 \right)=\frac{1}{3}=2\] \[\therefore \]Co-ordinate of centroid is (1, 2).You need to login to perform this action.
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