Verified Solution • 2025–26 Session moderate

QJEEM20Ma91bd: JEE Main 2020 Mathematics - Class 11 JEEM20Ma91bd Solution: Let C be the centroid of the triangle with vertices (3, –1),…

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 :

Multiple Choice Options

  • A (–9, –7)
  • B (9, 7)
  • C (7, 6)
  • D (–9, –6)

Step-by-Step Verified Solution

Centroid C (3+1+23,−1+3+43)\left( {{{3 + 1 + 2} \over 3},{{ - 1 + 3 + 4} \over 3}} \right) = (2, 2)

Point of intersection of lines x + 3y – 1 = 0

and 3x – y + 1 = 0 is P (−15,25)\left( { - {1 \over 5},{2 \over 5}} \right)

So, equation of line CP is 8x – 11y + 6 = 0

Point (–9, –6) satisfy this equation.

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