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KCET2007MathematicsStraight Lines

The orthocentre of the triangle with vertices A(0,0), B (0, 3 2 ), C(-5,0) is

Options

  1. A( 5 2 , 3 4 )
  2. B( -5 2 , 3 4 )
  3. C(-5, 3 2 )
  4. D(0,0)

Correct answer

D. (0,0)

Step-by-step solution

Let A O B is the given triangle. Slope of A B= 3 2 -0 0+5 = 3 10 Slope of B O= 0-0 0+5 =0 The equation of line passing through A and perpendicular to B O is y-0=-0 (x- 3 2 ) y=0 and equation of line passing through 0 and perpendicular to A B is y-0=- 10 3 (x-0) y=- 10 3 x The intersection point of Eqs. (i) and (ii) is (0,0) , which is the required orthocentre.

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