A) \[3x-2y=3\]
B) \[2x-3y=7\]
C) \[3x+2y=5\]
D) \[2x+3y=9\]
Correct Answer: D
Solution :
Let the third vertex be \[({{x}_{1}},\,{{y}_{1}})\] then Centroid\[(G)\equiv \left( \frac{{{x}_{1}}+2-2}{3},\,\frac{{{y}_{1}}-3+1}{3} \right)\] i.e., \[G\,\left( \frac{{{x}_{1}}}{3},\,\frac{{{y}_{1}}-2}{3} \right)\] Given, centroid of triangle moves on the line \[2x+3y=1\] \[\therefore \] \[2\,\left( \frac{{{x}_{1}}}{3} \right)+3\left( \frac{{{y}_{1}}-2}{3} \right)=1\] i.e., \[2{{x}_{1}}+3{{y}_{1}}=9\] Locus of \[({{x}_{1}},\,{{y}_{1}})\] is \[2x+3y=9\].You need to login to perform this action.
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