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JEE Main202227 Jul 2022Morning ShiftMathematicsStraight LinesActual

Let A 1 , 1 , B - 4 , 3 , C - 2 , - 5 be vertices of a triangle A B C , P be a point on side B C , and Δ 1 and Δ 2 be the areas of triangle A P B and A B C . Respectively. If Δ 1 : Δ 2 = 4 : 7 , then the area enclosed by the lines A P , A C and the x -axis is

Options

  1. A1 4
  2. B3 4
  3. C1 2
  4. D1

Correct answer

C. 1 2

Step-by-step solution

Plotting the given value in diagram we have, Now let P x , y be a point on B C , so area formed by △ A B P will be, Δ 1 = 1 2 x y 1 1 1 1 - 4 3 1 = 1 2 - 2 x - 5 y + 7 And area of triangle formed by △ A B C will be, Δ 2 = 1 2 1 1 1 - 4 3 1 - 2 - 5 1 = 36 2 Given Δ 1 Δ 2 = 4 7 ⇒ - 2 x - 5 y + 7 36 = 4 7 ⇒     14 x + 35 y = - 95           ⋯ 1 Equation of B C by two point form will be 4 x + y = - 13          

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