WBJEE 2012 Math Solved Paper

Let the vertices of R be (h, k)∴ Centroid of triangle is given by
(‌

x1+x2+x3

3

,‌

y1+y2+y3

3

)
ie, (‌

2+h−2

3

,‌

−3+1+k

3

)
ie, (‌

h

3

,‌

−2+k

3

)
Since, the point (‌

h

3

,‌

−2+k

3

) lies on the line 2x+3y=1, therefore the point (‌

h

3

,‌

−2+k

3

) must be satisfy the equation of the given line.
i.e,2(‌

h

3

)+3(‌

−2+k

3

)=1
⇒

2h−6+3k

3

=1
⇒2h−6+3k=3
⇒2h+3k=9
Replace h = x and k = y, We get the required locus of R.
i.e 2x+3y=9