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Question

The equation of the medians of a triangle formed by the lines x+y6=0,x3y2=0 and 5x3y+2=0, is

A
x=2,x+9y14=0 and 7x9y2=0
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B
x=2,x9y14=0 and 7x9y+2=0
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C
x=2,x+9y+14=0 and x9y2=0
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D
x=2,x9y14=0 and 7x+9y+2=0
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Solution

The correct option is A x=2,x+9y14=0 and 7x9y2=0
Let the given equation form a triangle ΔABC whose sides equations are:
AB:x+y6=0 ...(i)
BC:x3y2=0 ...(ii)
CA:5x3y+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(2,43)
So equation of the median passing through A will be
x=2
equation of the median passing through B will be
y43=4/3125(x2)x+9y=14
equation of the median passing through C will be
y+1=4/3+12+1(x+1)7x9y=2

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