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KVPY2013MathematicsStraight Lines

Consider a triangle ABC in the xy -plane with vertices A =(0,0), B =(1,1) and C =(9,1) . If the line x = a divides the triangle into two parts of equal area, then a equals

Options

  1. A3
  2. B3.5
  3. C4
  4. D4.5

Correct answer

A. 3

Step-by-step solution

area of P Q C= 1 2 area of A B C array l 1 2 (9-a) (1- a 9 )= 1 2 1 2 (8 1) (9-a)²=36 a=3 array

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