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 + 3 y - 1 = 0 and 3 x -y + 1 = 0. Then the line passing through the points C and P also passes through the point:

Question

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 + 3 y - 1 = 0 and 3 x -y + 1 = 0. Then the line passing through the points C and P also passes through the point: (A) ( - 9, -7 ) (B) ( -9 , -6 ) (C) (7, 6) (D) (9, 7)

Tardigrade Admin · Accepted Answer

Centroid of Δ = (2, 2) line passing through intersection of x + 3y - 1 = 0 and 3x - y + 1 = 0, be given by ∵ It passes through (2, 2) ⇒ 7+5λ=0 ⇒ λ=-(7/5) ∴ Required line is 8x - 11y + 6 = 0 ∵ (-9, -6) satisfies this equation.

Q. 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 $x + 3 y - 1 = 0$ and $3 x - y + 1 = 0$ . Then the line passing through the points $C$ and $P$ also passes through the point:

( - 9, -7 )

( -9 , -6 )

(7, 6)

(9, 7)

$C e n t ro i d o f Δ = (2, 2)$
line passing through intersection of
$x + 3 y - 1 = 0$ and
$3 x - y + 1 = 0$ , be given by
$∵$ It passes through $(2, 2)$
$\Rightarrow 7 + 5 λ = 0 \Rightarrow λ = - \frac{7}{5}$
$∴$ Required line is $8 x - 11 y + 6 = 0$
$∵ (- 9, - 6)$ satisfies this equation.

Q. 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:

( - 9, -7 )

( -9 , -6 )

(7, 6)

(9, 7)

CentroidofΔ=(2,2) line passing through intersection of x+3y−1=0 and 3x−y+1=0, be given by ∵ It passes through (2,2) ⇒7+5λ=0⇒λ=−57​ ∴ Required line is 8x−11y+6=0 ∵(−9,−6) satisfies this equation.

Q. 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 $x + 3 y - 1 = 0$ and $3 x - y + 1 = 0$ . Then the line passing through the points $C$ and $P$ also passes through the point: