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JEE Main201912 Apr 2019Evening ShiftMathematicsStraight LinesActual

A triangle has a vertex at ( 1 , 2 ) and the mid points of the two sides through it are ( - 1 , 1 ) and ( 2 , 3 ) . Then the centroid of this triangle is:

Options

  1. A1 3 , 1
  2. B1 , 7 3
  3. C1 3 , 2
  4. D1 3 , 5 3

Correct answer

C. 1 3 , 2

Step-by-step solution

Let co-ordinates of B = x 1 , y 1 ∴   x 1 + 1 2 =   - 1     &     y 1 + 2   2 = 1 ⇒   x 1 = - 3 ,       y 1 = 0 ∴ B = ( - 3 ,   0 ) Let co-ordinates of C = x 2 , y 2 ∴   x 2 + 1 2 = 2     &     y 2 + 2 2 = 3 ∴   C = 3 ,   4 Let centroid G = h , k h = 1 + x 1 + x 2 3 = 1 - 3 + 3 3 = 1 3     k = 2 + y 1 + y 2 3 = 2 + 0 + 4 3 = 2 ∴     Centroid, G = 1 3 , 2

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