question_answer

lf A(2,-3) and B(-2,1) are two vertices of a triangle and third vertex moves on the line \[2x+3y=9,\] then the locus of the centroid of the triangle is :     AIEEE  Solved  Paper (Held On 11 May  2011)

A) \[xy=1\]         

B) \[2x+3y=1\]       

C)  \[2x+3y=3\]

D) \[2x3y=1\]

Correct Answer: B

Solution :

                              \[\alpha =3h\] \[\beta -2=3k\] third vertex on the line \[2x+3y=9\] \[2\alpha +3\beta =9\] \[2(3h)+3(3k+2)=9\] \[2h+3k=1\] \[2x+3y-1=0\]