A) \[3x-2y=3\]
B) \[2x+3y=9\]
C) \[2x-3y=7\]
D) \[3x-2y=5\]
Correct Answer: B
Solution :
Let coordinate of third vertex be \[C({{x}_{1}},\,{{y}_{1}})\] Then, centroid of triangle \[=\left( \frac{2+(-2)+{{x}_{1}}}{3},\frac{-3+1+{{y}_{1}}}{3} \right)=\left( \frac{{{x}_{1}}}{3},\frac{{{y}_{1}}-2}{3} \right)\] Since, centroid of this triangle moves on the line \[2x+3y=1\] \[\therefore \] \[2\left( \frac{{{x}_{1}}}{3} \right)+3\left( \frac{{{y}_{1}}-2}{3} \right)=1\] \[\Rightarrow \] \[2{{x}_{1}}+3{{y}_{1}}-6=3\] \[\Rightarrow \] \[2{{x}_{1}}+3{{y}_{1}}=9\] Hence, the locus of the vertex C is the line \[2x+3y=9\]
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