\ The equation of the medians of a triangle formed by the lines `x+y-6=0, x-3y-2=0` and `5x-3y+2=0` is

Explanation

Let the given equation form a triangle ΔABC whose sides equations are:

AB:x+y−6=0 ...(i)

BC:x−3y−2=0 ...(ii)

CA:5x−3y+2=0 ...(iii)

So intersection point of AB,BC is B(5,1)

similarly for BC,CA and CA,AB we get C(−1,−1) and A(2,4) respectively

Let G be the centriod, then all the medians will pass through G only and G≡(2,4/3)

So equation of the median passing through A will be
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