A) 2x + 3y = 9
B) 2x - 3y = 7
C) 3x+2y=5
D) 3x-2y=3
Correct Answer: A
Solution :
Let (x, y) be the coordinates of vertex C and \[({{x}_{1}},{{y}_{1}})\] be the coordinates of centroid of the triangle. \[\therefore \] \[{{x}_{1}}=\frac{x+2-2}{3}\] and \[{{y}_{1}}=\frac{y-3+1}{3}\] \[\Rightarrow \] \[{{x}_{1}}=\frac{x}{3}\] and \[{{y}_{1}}=\frac{y-2}{3}\] Since, the centroid lies on the line 2x + 3y = 1. \[\therefore \] \[2{{x}_{1}}+3{{y}_{1}}=1\] \[\Rightarrow \] \[\frac{2x}{3}+3\frac{(y-2)}{3}=1\] \[\Rightarrow \] \[2x+3y-6=3\] \[\Rightarrow \] \[2x+3y=9\]which is the required locus of vertex C.
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