question_answer

Let \[A-(-3,2)\] and \[B-(-2,1)\] be the vertices of a triangle ABC. If the centroid of triangle ABC lies on the line \[3x+4y+2=0\], then the locus of vertex C is

A) \[4x+3y+5=0\]                  

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

C) \[4x+3y+3=0\]                  

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

Correct Answer: B

Solution :

\[\therefore \]  \[3\left( \frac{h-5}{3} \right)+4\left( \frac{k+3}{3} \right)+2=0\] \[\Rightarrow 3(h-5)+4(k+3)+6=0\] \[\therefore \]  The locus of\[C(h,\,\,k)\]is\[3x+4y+3=0\]