JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Straight Lines

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) $(- 9, - 6)$ ✓ Correct
(C) $(7, 6)$
(D) $(9, 7)$

Answer: (B)

Solution

The centroid is

C = (\frac{3 + 1 + 2}{3}, \frac{- 1 + 3 + 4}{3}) = (2, 2)

. Solving

x + 3 y - 1 = 0

together with

3 x - y + 1 = 0

gives

P = (- \frac{1}{5}, \frac{2}{5})

. The line through

C

and

P

has slope

\frac{2 - 2/5}{2 + 1/5} = \frac{8}{11}

, so its equation is

8 x - 11 y + 6 = 0

. Testing the candidate points,

(- 9, - 6)

satisfies it, since

8 (- 9) - 11 (- 6) + 6 = - 72 + 66 + 6 = 0

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Single correct option

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