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Let x 1 , y 1 ,   x 2 , y 2 ,   x 3 , y 3 and x 4 , y 4 are four points which are at unit distance from the lines 3 x - 4 y + 1 = 0 and 8 x + 6 y + 1 = 0 , then the value of ∑ i = 1 4 x i ∑ i = 1 4 y i is equal to

Options

  1. A2
  2. B– 2
  3. C1
  4. D– 1

Correct answer

B. – 2

Step-by-step solution

Point of intersection of 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 4 y i = 4 1 10 = 2 5 ⇒ ∑ i = 1 4 x i ∑ i = 1 4 y i = - 4 5 2 5 = - 2

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