If the Let ABC be a triangle having orthocentre and circumcentre at (9, 5) and (0, 0) respectively. equation of side BC is `2x-y = 10`, then find the possible coordinates of vertex A .

Explanation

let the coordinates of point G is`(2*0+9*1)/(2+1), (2*0+5*1)/(2+1)`

`=(x_1+x_2+x_3)/3 , (y_1+y_2+y_3)/3`

`a= (3,5/3) =(x_1+x_2+x_3)/3 , (y_1+y_2+y_3)/3 `

`x_1+x_2+x_3=9`

`y_1+y_2+y_3=5`

`D(h,k)` lie on line BC

so will satisfy its eqn `2h-k=0`

slope of `C'D* slope of BC =-1`

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