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NTA Abhyas JEE Main2020MathematicsStraight LinesPractice

The point A divides the line segment joining the points ( - 5,1 ) and ( 3,5 ) in the ratio k : 1 internally and the coordinates of points B and C are 1,5 and 7 , - 2 respectively. If the area of ∆ A B C is 2 sq. units, then the sum of all the values of k is equal to

Options

  1. A32 9
  2. B7
  3. C94 9
  4. D31 9

Correct answer

C. 94 9

Step-by-step solution

A ≡ 3 k - 5 k + 1 , 5 k + 1 k + 1 Area of ∆ A B C = 2 sq. u n i t s ⇒ 1 2 3 k - 5 k + 1 5 + 2 + 1 - 2 - 5 k + 1 k + 1 + 7 5 k + 1 k + 1 - 5 = ± 2 ⇒ 14 k - 66 = ± 4 k + 1 ⇒ k = 7 or 31 9

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