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99 Percentile Qs Bank for JEE MainMathematicsStraight Lines

Let A - 1 , 1 ,   B 3 , 4 and C 2 , 0 be given three points. A line y = m x ,   m > 0 , intersects lines A C and B C at point P and Q respectively. Let A 1 and A 2 be the areas of Δ A B C and Δ P Q C respectively, such that A 1 = 3 A 2 , then the value of m is equal to :

Options

  1. A4 15
  2. B1
  3. C2
  4. D3

Correct answer

B. 1

Step-by-step solution

P ≡ x 1 , m x 1 Q ≡ x 2 , m x 2 A 1 = 1 2 3 4 1 2 0 1 - 1 1 1 = 13 2 A 2 = 1 2 x 1 m x 1 1 x 2 m x 2 1 2 0 1 A 2 = 1 2 2 m x 1 - m x 2 = m x 1 - x 2 A 1 = 3   A 2 ⇒ 13 2 = 3   m x 1 - x 2 ⇒    x 1 - x 2 = 16 6   m A C :   x + 3   y = 2 B C :   y = 4   x - 8 P : x + 3 y = 2   &   y = m x ⇒ x 1 = 2 1 + 3 m Q :   y = 4 x - 8   &   y = m x ⇒ x 2 = 8 4 - m x 1 - x 2 = 2 1 + 3 m - 8 4 - m = - 26   m 1 +

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