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If the centroid and circumcenter of a triangle are 3 , 3 , 6 , 2 , respectively, then the orthocentre of the triangle is _____.

Options

  1. A9 , 5
  2. B3 , - 1
  3. C- 3 , 1
  4. D- 3 , 5

Correct answer

D. - 3 , 5

Step-by-step solution

The orthocenter, centroid and circumcenter of the triangle are collinear and lie on the line called Euler Line. Also the centroid divides the line joining orthocenter and circumcenter in the ratio 2   :   1 . So centroid 3 , 3 would be dividing x , y and 6 , 2 in the ratio of 2   :   1 . So, 12 + x 3 = 3 , therefore x = 9 - 12 =   - 3 , and 4 + y 3 = 3 , therefore y = 5 . Hence, - 3 ,   5 is the answer.

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