If in triangle ABC, A=(1, 10), circumcentre=`(-1/3, 2/3)` and orthocentre=`(11/3,4/3)` then the co-ordinates of mid-point of side opposite to A is:

Options

A. `(1,-11//3)`
B. `(1//5)`
C. `(1,-3)`
D. `(1,6)`

Answer

A

Explanation

Circumcenter `O-=(-1//3,2//3)` and orthocenter `H-=(11//3,4//3)`

Therefore the coordinates of G are `(1,8//9)`. Now,the point A is `(1,10)` as G is `(1,8//9)`.
Also, `AD:DG=3:1`,
`therefore D-=((3-1)/(3-1),(8//3-10)/(3-1))-=(1,-11//3)`
`therefore D=(3-1)/(2)=1,D_(y)=(8//3-10)/(2)=-11/3`
Hence, the coordinates of the midpoint of BC are `(1,-11//3)` .