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AP EAMCET2016MathematicsStraight Lines

The mid-point of the line segment joining the centroid and the orthocentre of the triangle whose vertices are (a, b),(a, c) and (d, c) , is

Options

  1. A( 5 a+d 6 , b+5 c 6 )
  2. B( a+5 d 6 , 5 b+c 6 )
  3. C(a,c)
  4. D(0,0)

Correct answer

A. ( 5 a+d 6 , b+5 c 6 )

Step-by-step solution

The vertices of the triangle are given as A ( a , b ), B ( a , c ) and C ( d , c ) Centroid of ABC = ( a+a+d 3 , b+c+c 3 ) ( 2 a+d 3 , 2 c+b 3 ) Since, x -coordinate of point A and B are same. Also y -coordinate of point B and C are same so it forms a right angle triangle. Orthocentre of ABC is ( a , c ) Mid-point of centroid and orthocentre is = ( 2 a+d 3 +a 2 , 2 c+b 3 +c 2 )= ( 5 a+d 6 , 5 c+b 6 )

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