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Let C be the centroid of the triangle with vertices (3, -1) ,(1, 3) and (2, 4). Let P be the point of intersection of the lines x+3y-1=0 and 3x-y+1=0. Then the line passing through the points C and P also passes through the point:

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a

7,6

b

−9,−6

c

9,7

d

−9,−7

answer is B.

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Detailed Solution

Given C=3+1+23,-1+3+43=(2,2) The line passing through P and C can be written as (x+3y-1)+λ(3x-y+1)=0 C lies on it ⇒7+5λ=0⇒λ=-75 So, the equation will be 5(x+3y-1)-7(3x-y+1)=0 or -2(8x-11y+6)=0(-9,-6) will lie on this line

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Let C be the centroid of the triangle with vertices (3, -1) ,(1, 3) and (2, 4). Let P be the point of intersection of the lines x+3y-1=0 and 3x-y+1=0. Then the line passing through the points C and P also passes through the point: