Orthocenter and circumcenter of a `"Delta"A B C` are `(a , b)a n d(c , d)` , respectively. If the coordinates of the vertex `A` are `(x_1,y_1),` then find the coordinates of the middle point of `B Cdot`

Explanation

Given are the orthocentre `H(a,b)` and the circumcentre `O(c,d)`.

`therefore` Centroid, `G=((2c+a)/(2+1),(2d+b)/(2+1))-=((2c+a)/(3),(2d+b)/(3))`

Now, centroid G divides AD in the ratio `2:`, where D is the midpoint of BC.
`therefore (2c+a)/(3)=(2x_2+x_1)/(3)`
and `(2d+b)/(3)=(2y_2+y-1)/(3)`
`therefore x_2=(2c+a -x_1)/(2),y_2=(2d+b-y_1)/(2)`