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The line 3 x + 2 y = 24 meets the y -axis at A & the x -axis at B . The perpendicular bisector of AB meets the line through ( 0 , - 1 ) parallel to x -axis at C . Then the area of the triangle ABC is

Correct answer

91

Step-by-step solution

Equation of CD ⇒ 2 x - 3 y = λ .....(1) it passes through ( 4 ,   6 ) then λ = - 1 0 2 x - 3 y + 1 0 = 0 ....(2) coordinates of C  - 1 3 2 , - 1 Now, the area of the triangle, Δ = 1 2 0 1 2 1 8 0 1 - 1 3 2 - 1 1 = 1 2 0 - 1 2  8 + 1 3 2 + 1 - 8 = 1 2 - 6 2 9 - 8 = 9 1

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