First slide

Cartesian plane

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

Moderate

A

$(7, 6)$
B

$(- 9, - 6)$
C

$(9, 7)$
D

$(- 9, - 7)$

Solution

$Given C = (\frac{3 + 1 + 2}{3}, \frac{- 1 + 3 + 4}{3}) = (2, 2)$
$\begin{array}{l} The line passing through P and C can be written as (x + 3 y - 1) + λ (3 x - y + 1) = 0 \\ C lies on it \Rightarrow 7 + 5 λ = 0 \Rightarrow λ = - \frac{7}{5} \end{array}$
$So, the equation will be 5 (x + 3 y - 1) - 7 (3 x - y + 1) = 0 or - 2 (8 x - 11 y + 6) = 0$
$(- 9, - 6) will lie on this line$

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