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Let in a ∆ A B C , vertex A , the circumcentre S and the orthocentre H are 1 , 10 , - 1 3 , 2 3 and 11 3 , 4 3 respectively, then mid-point of the side B C is

Options

  1. A1 , - 11 3
  2. B1 , - 22 3
  3. C2 , - 11 3
  4. D- 1 , 11 3

Correct answer

A. 1 , - 11 3

Step-by-step solution

We know that centroid divides orthocentre and cirumcentre in the ratio 2 : 1 Hence, centroid G is - 2 3 + 11 3 3 , 4 3 + 4 3 3 ⇒ G = 1 , 8 9 Let, D is the mid-point of side B C then G also divides A and D in the ratio 2 : 1 2 h + 1 3 = 1 and 2 k + 10 3 = 8 9 ⇒ h = 1 and k = - 11 3 ⇒ D = 1 , - 11 3

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