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Q)

The orthocenter of the triangle formed by the points (0,0) (8,0) and (4,6)


( A ) (4,8/3)
( B ) (-4,3)
( C ) (3,4)
( D ) (4,3)

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A)

Orthocenter is the point of intersection of altitudes of a triangle and centroid divides the straight line formed by joining circumcenter and the orthocenter in the ratio 2:1.
Let the vertices of the triangle be O (0, 0), A(8, 0) and B(4, 6)
The equation of an altitude through O and perpendicular to AB is y = 2/3x and similarly the equation of an altitude through A and perpendicular to OB is 2x + 3y = 16. Now find the point of intersection of these two straight line


 

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