question_answer

                Let A (-3,2) and B(-2,1) be the vertices of a triangle ABC. If the centroid of this triangle lies on the line \[3x+4y+2=0,\] the vertex C lies on the line:     JEE Main Online Paper ( Held On 25  April 2013 )

A)                 \[4x+3y+5=0\]  

B)                                        \[3x+4y+3=0\]

C)                                        \[4x+3y+3=0\]  

D)                                        \[3x+4y+5=0\]

Correct Answer: B

Solution :

                Let \[C=({{x}_{1}},{{y}_{1}})\] Centroid,\[E=\left( \frac{{{x}_{1}}-5}{3},\frac{{{y}_{1}}+3}{3} \right)\] Since centroid lies on the line \[3x+4y+2=0\] \[\therefore \]\[3\left( \frac{{{x}_{1}}+5}{3} \right)+4\left( \frac{{{y}_{1}}+3}{3} \right)+2=0\] \[\Rightarrow \]\[3{{x}_{1}}+4{{y}_{1}}+3=0\] Hence vertex \[({{x}_{1}},{{y}_{1}})\]lies on the line \[3x+4y+3=0\]