Q.

The orthocentre of triangle formed by points 0,03,42,3 is −k,k then k is

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answer is 18.

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Detailed Solution

The ortho centre of a triangle is the point of concurrence of the altitudes The slope of the line joining 0,0,2,3  is    m=32The equation of the altitude from 3,4 is y−4=−23x−33y−12=−2x+62x+3y−18=0Point −k,k lies on the line  2x+3y−18=0 It implies   −2k+3k−18=0⇒k=18
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