Median through C is x=4 So the x coordianate of C is 4 . let C≡(4,y), then the midpoint of A(1,2) and C(4,y) is D which lies on the median through B.
∴D≡(
1+4
2
,
2+y
2
) Now ,
1+4+2+y
2
=5⇒y=3 So, C≡(4,3) The centroid of the triangle is the intersection of the mesians. Here the medians x=4 and x+4 and x+y=5 intersect at G(4,1) The area of triangle ∆ABC=3×∆AGC =3×