C is 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 a line which passes through both points C and P would also passes through the point_______
=2 ∴ Centroid (x,y)=(2,2) Point of intersection of line x+3y−1=0 and 3x−y+1=0 is obtained by solving these equation for x and y, we obtain P(α,β)=P(
−1
5
,
2
5
) Equation of line passes through C(2,2) and P(
−1
5
,
2
5
) is given as
y−2
2
5
−2
=
x−2
−
2
5
−2
⇒
y−2
−3
=
x−2
−11
⇒11(y−2)=8(x−2y) ⇒11y−8x=6 ...(i) Among the given option only (−9,−6) satisfy Eq. (i).