In a triangle ABC, coordinates of A are (1,2) and the equations of the medians through B and C are respectively, x+y=5 and x=4. Then area of ΔABC (in sq.units) is

We draw the triangle ABC by given data belowSo, centroid G is (4,1)Let coordinate of B(α,5−α) and B(4,β).Mid-point AB lies of median of C and has value Mα+12,1−α2So, α+12=4⇒α=7Similarly, mis-point AC lies of median of B and has value N52,β+22 52+β+22=5⇒β=3Therefore, area of ΔABC is 121(−2−3)+7(3+2)+4(2+2)=12-5+7+16=9