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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

Let A x 1 , y 1 , B x 2 , y 2 , C x 3 , y 3 and D x 4 , y 4 are four points which are at equal distance from the lines 3 x - 4 y + 1 = 0 and 8 x + 6 y + 1 = 0 . The mean of the coordinates of the centroids of ∆ A B C , ∆ B C D , ∆ C D A and ∆ D A B are

Options

  1. A- 4 5 , 2 5
  2. B- 1 5 , 1 10
  3. C- 3 5 , 3 10
  4. D- 4 15 , 2 15

Correct answer

B. - 1 5 , 1 10

Step-by-step solution

Point of intersection of the lines 3 x - 4 y + 1 = 0 and 8 x + 6 y + 1 = 0 is - 1 5 , 1 10 Now, ∑ i = 1 4 x i = 4 - 1 5 = - 4 5 And, ∑ i = 1 8 y i = 4 1 10 = 2 5 Mean of the centroids of ∆ A B C , ∆ B C D , ∆ C D A and ∆ D A B is ∑ i = 1 4 x i 4 , ∑ i = 1 4 y i 4 = - 1 5 , 1 10

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